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(1972). Critical exponents in 3.99 dimensions. Physical Review Letters, 28(4), 240–243.","status":"active","vx_hash":"319a45d83aa4a73b66d5c64ae1508e83114b0884ee2e6493916205828896100d","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"ee815dac5cc04619daa818378901e9d91efe0396e079a3722f5b87e1e8e74ebc","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"2e017d0a93dccfe3f89215a63be0efe5d677a5a12d4d61cfba857dc160c0cb16","detail":{"divided_from":"body","block":6,"kind":"p"},"prev":"genesis","hash":"ee815dac5cc04619daa818378901e9d91efe0396e079a3722f5b87e1e8e74ebc"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d6"},{"id":"d7","kind":"p","type":null,"order":7,"text":"The abstract states: \"Critical exponents are calculated for dimension d = 4 − ε with ε small, using renormalization-group techniques. To order ε the exponent γ is 1 + ε/6 for an n-vector model with n = 1.\"","status":"active","vx_hash":"34a7e1ab877e3ce1c643e8beee5ab259de24b814b91f2c5e4ae5f6c63ca27272","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"8628fc3a90a8180ee6c1f4c2e220116976a1225fa67bb229f8cccf4ab26edb86","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"800ef1038f96a0691e80fd0beff7d53da48e00ef1df791b862ff11af1006373f","detail":{"divided_from":"body","block":7,"kind":"p"},"prev":"genesis","hash":"8628fc3a90a8180ee6c1f4c2e220116976a1225fa67bb229f8cccf4ab26edb86"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d7"},{"id":"d8","kind":"p","type":null,"order":8,"text":"The paper derives the beta function for the quartic coupling and locates the nontrivial fixed point at order ε. It then computes the eigenvalue spectrum that yields the exponents.","status":"active","vx_hash":"fd3c6b94550fe071e9f4a0c41b3a26040227ee686b2fe6aed1d583987f9f53de","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"b0b515e5a10d26ce99a934605d11878d680654ca50dec363443eed19f5364964","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"459f13f3a1165dde773e123d8808826db1c751358b1baa0d93f7a04ec978002d","detail":{"divided_from":"body","block":8,"kind":"p"},"prev":"genesis","hash":"b0b515e5a10d26ce99a934605d11878d680654ca50dec363443eed19f5364964"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d8"},{"id":"d9","kind":"p","type":null,"order":9,"text":"No page-numbered quotes beyond the abstract are required for verification because the letter format places all derivations in the main text of the three-page article.","status":"active","vx_hash":"36290d6c7b4f6827c016a4cd445218a196b2c143d20c708589d14c736514447c","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"930b9022c7143e91ab196f3095c09c9d1ab25419c9775d2a056cf620b6626d82","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"e8d3e682c3d1f4b741756b7a4bc4f4436feedbd8be8a3b6bc9b4fb97a5e7d6c6","detail":{"divided_from":"body","block":9,"kind":"p"},"prev":"genesis","hash":"930b9022c7143e91ab196f3095c09c9d1ab25419c9775d2a056cf620b6626d82"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d9"},{"id":"d10","kind":"h","type":null,"order":10,"text":"## Convergence patterns the work touches","status":"active","vx_hash":"a156be8455f4a37e04712c76ee5bfa73ab4a3d7bf2c63c77bc593a251c1d45f9","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"5e07bfc17280ffc51701c8ab212f4ed6de687e4f0f7c383f61af9a2886678d0d","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"b6d9d72e19d6be3f78a04abcf3c3cfe506c7689994f1b7454a69a2a2de2e7f44","detail":{"divided_from":"body","block":10,"kind":"h"},"prev":"genesis","hash":"5e07bfc17280ffc51701c8ab212f4ed6de687e4f0f7c383f61af9a2886678d0d"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d10"},{"id":"d11","kind":"p","type":null,"order":11,"text":"The paper evidences scale invariance. Critical exponents remain unchanged under rescaling of length.","status":"active","vx_hash":"1d8937f878f05144801e7518873c8ba6056b3706aeda32cc3428f3589141d153","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"b1cd5a822f75cff8aa0aee7fcdd7abefa36b9f04f3aa6af072d867ec1ebbcac7","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"7e5ecd79359e778c2b0a23f2f03537a37f250fa6befa2837db8f03da5b13c3f4","detail":{"divided_from":"body","block":11,"kind":"p"},"prev":"genesis","hash":"b1cd5a822f75cff8aa0aee7fcdd7abefa36b9f04f3aa6af072d867ec1ebbcac7"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d11"},{"id":"d12","kind":"p","type":null,"order":12,"text":"It evidences flow networks. The renormalization-group transformation defines a flow in coupling-constant space that converges to a fixed point.","status":"active","vx_hash":"9f7bf12cd93251e55721143876a2e8a88e8d531ab28059dbb6d0d43418dccff8","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"55f0ddc5fda24a6b946f76f9c05e217cc6a4f8734d77d27a748417f4a9764d8e","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"302ee792f47421eb235ca7f3c1b185efdd6f8f28fccc68d1b8187e3d76749483","detail":{"divided_from":"body","block":12,"kind":"p"},"prev":"genesis","hash":"55f0ddc5fda24a6b946f76f9c05e217cc6a4f8734d77d27a748417f4a9764d8e"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d12"},{"id":"d13","kind":"p","type":null,"order":13,"text":"It evidences symmetry breaking. The ordered phase below the critical temperature breaks the continuous symmetry of the n-vector model.","status":"active","vx_hash":"5fcd258fe4c0435f0f86c7929f4767c2694b919f6a71b537218867f90717171a","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"cf6c5740e09a592a83606542b9380a2e3812cab7ddc8d1d6fb82bfac9b522851","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"8f36d66dea7a3cf8e6fd21fea405cbdba920a942fe34d270ef14c7eca5958116","detail":{"divided_from":"body","block":13,"kind":"p"},"prev":"genesis","hash":"cf6c5740e09a592a83606542b9380a2e3812cab7ddc8d1d6fb82bfac9b522851"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d13"},{"id":"d14","kind":"p","type":null,"order":14,"text":"It evidences bounded chaos. Fluctuations remain controlled near the upper critical dimension.","status":"active","vx_hash":"616991a712d5b2cbe3ec6a08d38854525c175ad07d1d3563ec65a70daf52195f","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"60d4b8d77c6b0e977e0f60c22128bd615732234f2396bb8b9cfecab4202f5754","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"c1782db0dad2959e388b93b5a0c8bc1fd08dbfb563ebccab50b4fcb10e70af83","detail":{"divided_from":"body","block":14,"kind":"p"},"prev":"genesis","hash":"60d4b8d77c6b0e977e0f60c22128bd615732234f2396bb8b9cfecab4202f5754"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d14"},{"id":"d15","kind":"p","type":null,"order":15,"text":"These patterns appear as mathematical consequences of the fixed-point equations rather than as external assumptions.","status":"active","vx_hash":"eb8ca1c56af42c9dced0d3867e512ec96189d0be6061fc0d89bcd43b707c0b09","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"31637268b32074846e6475094d9d571a1d1e0dac99204b030651eebee4f42134","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"24a17e57bf9c7f9860099ddbd2c99d25582a4d85a81abeb9827e0758d9ce8b8f","detail":{"divided_from":"body","block":15,"kind":"p"},"prev":"genesis","hash":"31637268b32074846e6475094d9d571a1d1e0dac99204b030651eebee4f42134"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d15"},{"id":"d16","kind":"h","type":null,"order":16,"text":"## Distance from the full OIP/GRAIN synthesis","status":"active","vx_hash":"606fafdebee141cf8488a7071920bb06f901c540fe3ee158eeb9a681266f3db6","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"6f349e4e86fafe3c6d2f876e1edf49f234ab401771b7722fe91f829d25980f74","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"78b248fc09f46aa233e0ee4e7ccd8141328a45bdb7ef545daf36dd82e28468ad","detail":{"divided_from":"body","block":16,"kind":"h"},"prev":"genesis","hash":"6f349e4e86fafe3c6d2f876e1edf49f234ab401771b7722fe91f829d25980f74"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d16"},{"id":"d17","kind":"p","type":null,"order":17,"text":"The work lies at mechanistic distance. It supplies a concrete route from microscopic Hamiltonians to universal macroscopic exponents through explicit flow equations.","status":"active","vx_hash":"d1feb746c1ccf85efb418c3ec9c605e9b23289e98afda6932a407001022c9db7","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"60a49c4fbefa78cc07ebed31782e3b7575823e7f9de45a7283e3d6eba8e5b88b","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"325f510afc089cba7e45f236c4b7c382de16dbddb1b56c76882ed4f77040c76e","detail":{"divided_from":"body","block":17,"kind":"p"},"prev":"genesis","hash":"60a49c4fbefa78cc07ebed31782e3b7575823e7f9de45a7283e3d6eba8e5b88b"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d17"},{"id":"d18","kind":"p","type":null,"order":18,"text":"It supports the grain claim. Universal patterns arise reliably from energy flows at criticality across a continuous range of dimensions.","status":"active","vx_hash":"6f160975d067a1ac38c90482fb65179075731792810245dfccc11084e47b4bf1","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"421e3902060c3e8d9b617837d4c484106c8e751f7de79f3360f0830413bba7d9","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"9a52f88cd23e36ca3ade8efc7a18f9233dc98fd92e8e84a9c42ab830e75e2c9f","detail":{"divided_from":"body","block":18,"kind":"p"},"prev":"genesis","hash":"421e3902060c3e8d9b617837d4c484106c8e751f7de79f3360f0830413bba7d9"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d18"},{"id":"d19","kind":"p","type":null,"order":19,"text":"It does not address the Ladder from difference to mind. The analysis stops at statistical mechanics.","status":"active","vx_hash":"44a4ea8e573cb1432018465c4679967dfe2e0946ecb4f59f61122ee8d1e5a302","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"397780e60a6f205ce64dd4fc99ed027c9fca81218d468fe7c2d262bceb80eed9","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"0e46a3e599c1b0c674bc7fbb6c70af98478d1581d6155dda3ca570864efb798e","detail":{"divided_from":"body","block":19,"kind":"p"},"prev":"genesis","hash":"397780e60a6f205ce64dd4fc99ed027c9fca81218d468fe7c2d262bceb80eed9"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d19"},{"id":"d20","kind":"p","type":null,"order":20,"text":"It does not address the Mirror Layer. No observer-system recursion appears.","status":"active","vx_hash":"43dc056664cec319ca835005e271e4cc4d1f79292e6346666dbbf6d139b530a8","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"c04c6de80ddfc78047691e2767c66989634b4a8f97aca695422d7fcaee7083d4","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"89836175ba795c40dcf22dcb9d256884541c4907a5cf391e3ea3d83935832273","detail":{"divided_from":"body","block":20,"kind":"p"},"prev":"genesis","hash":"c04c6de80ddfc78047691e2767c66989634b4a8f97aca695422d7fcaee7083d4"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d20"},{"id":"d21","kind":"p","type":null,"order":21,"text":"The synthesis therefore receives partial support at the level of structural emergence but receives no extension to life or cognition.","status":"active","vx_hash":"7a47c52c1ad2bae15e9e6df3bf3e87ca96d3dfb08aeb98126287f0ffbda1d6ec","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"0f7cc14e5e16c38170c19a66cb240157af9ca257c28150c034d608bccc3fa5e5","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"c21ad304e40925ec0c3040e23f5d123b2747b6d855536dbd4d179f2ab6fc475a","detail":{"divided_from":"body","block":21,"kind":"p"},"prev":"genesis","hash":"0f7cc14e5e16c38170c19a66cb240157af9ca257c28150c034d608bccc3fa5e5"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d21"},{"id":"d22","kind":"h","type":null,"order":22,"text":"## Honest limits and disconfirming edges","status":"active","vx_hash":"cd08510df5a77b48aebb042a9dc04d10ab69fc5c72a87004641d3eba2c3147b6","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"eee14a18d20a4c67b453b2457c19e2dd4122e617e51c8956e5610bb940ad6ab8","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"a4ff4542a1095d01f9181ea0192500270e1b6d9e89daf971127e5a818cfedd26","detail":{"divided_from":"body","block":22,"kind":"h"},"prev":"genesis","hash":"eee14a18d20a4c67b453b2457c19e2dd4122e617e51c8956e5610bb940ad6ab8"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d22"},{"id":"d23","kind":"p","type":null,"order":23,"text":"The expansion is perturbative and valid only for small ε. Direct application to three dimensions requires Borel resummation whose convergence remains unproven to all orders.","status":"active","vx_hash":"4ea7b2172378b905599fb337ca0a462a3c6725addc6f6b1401891f08b8f7f0c7","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"bad1688ff1c4882ebc410343ccc87f1c8a79104576f6d2c674cffdc8430175b1","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"f33bffca3dc21de0a26d9309a68f0efe80e987a691a046a072a4f5e199b5e2c1","detail":{"divided_from":"body","block":23,"kind":"p"},"prev":"genesis","hash":"bad1688ff1c4882ebc410343ccc87f1c8a79104576f6d2c674cffdc8430175b1"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d23"},{"id":"d24","kind":"p","type":null,"order":24,"text":"The calculation assumes a local quartic interaction. Long-range interactions or higher-order terms alter the fixed-point structure.","status":"active","vx_hash":"29d124e09a02406e36932811bd464356932cd0fa826b01e437a80281b3aaac43","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"df9f824b7ab4e7cc87ef955969bd947ce8a5478c4375f3028f5e0708079d627e","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"1285c5a1c7ef98bb44b445d40cb0e13db8ea392d9418fc28165ad078a3305eaf","detail":{"divided_from":"body","block":24,"kind":"p"},"prev":"genesis","hash":"df9f824b7ab4e7cc87ef955969bd947ce8a5478c4375f3028f5e0708079d627e"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d24"},{"id":"d25","kind":"p","type":null,"order":25,"text":"Reductionist objections apply. The exponents describe ensemble averages; they do not predict individual trajectories or deterministic outcomes.","status":"active","vx_hash":"266c6ff1414cbc87967769a0f0288c8a7bde43904bbf592fa9d8e349c0f393bd","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"7f57d65edf13f27d7d546c46bcfa1a46a7e2278183c2ac6213187edd8004a55b","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"0d28a9be2577b979d16156a5cbbbd442bc964a9b8332c37b849dcff7594ddc08","detail":{"divided_from":"body","block":25,"kind":"p"},"prev":"genesis","hash":"7f57d65edf13f27d7d546c46bcfa1a46a7e2278183c2ac6213187edd8004a55b"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d25"},{"id":"d26","kind":"p","type":null,"order":26,"text":"No empirical human data exist. All results are mechanistic derivations from the renormalization 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or protocol-level invocation.","status":"active","vx_hash":"cc8e39759f5d7cf68c74d7099b9a3b74b8fd085fb8a6b3b341e9395f7880a478","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"b0003171812e15896435503bd8475caa29e2e59ce521bbde4a0455650f483bad","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"6f811b8e2710e46de8f794407f4b7d312bf0d99a5ef93e1dc71074f62166e9ac","detail":{"divided_from":"body","block":27,"kind":"p"},"prev":"genesis","hash":"b0003171812e15896435503bd8475caa29e2e59ce521bbde4a0455650f483bad"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d27"},{"id":"d28","kind":"h","type":null,"order":28,"text":"## Relation to sibling articles","status":"active","vx_hash":"1c8c960e303a4b071d3c068e7c2961c19d222f50be25ba1d4fbb3af41018e508","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"1f9d40b120aff609b8c818670f3735e61947c5504fb3df6c9c743ceec0cf8c6c","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"f8edac880e579e5ca87321abaa626efbf1b7980bed924e246edd5dcd07c15261","detail":{"divided_from":"body","block":28,"kind":"h"},"prev":"genesis","hash":"1f9d40b120aff609b8c818670f3735e61947c5504fb3df6c9c743ceec0cf8c6c"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d28"},{"id":"d29","kind":"p","type":null,"order":29,"text":"See /a/oip-the-ladder for the step from structure to memory.","status":"active","vx_hash":"35cebb47df76f2ed815c0afc198e76105f8f650c962b40f720501086c4493265","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"f4686b13678064cacd365552128353bbe116f6c0c05d46258808d16d9ad0544f","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"c66ce86a8806d3cae747a06d7a6b079af64d4e4e57a2b8f45f6fee60045f083e","detail":{"divided_from":"body","block":29,"kind":"p"},"prev":"genesis","hash":"f4686b13678064cacd365552128353bbe116f6c0c05d46258808d16d9ad0544f"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d29"},{"id":"d30","kind":"p","type":null,"order":30,"text":"See /a/oip-principles for the definition of flow-to-structure.","status":"active","vx_hash":"4cea9fcd31970262ac104f6a5ff6c7463c8bcf772ce79b2cd5260a7b2170578a","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"7b9d35c0849ee27d868dc01cd21ec64b096636b8c4d3f06439082f654b8187be","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"a459ef073a7f31a375b9eae2b095294bea60454588df88ae7f9fa07bccd73661","detail":{"divided_from":"body","block":30,"kind":"p"},"prev":"genesis","hash":"7b9d35c0849ee27d868dc01cd21ec64b096636b8c4d3f06439082f654b8187be"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d30"},{"id":"d31","kind":"p","type":null,"order":31,"text":"See /a/oip-the-mirror-layer for observer recursion.","status":"active","vx_hash":"eda412f71e29678edd61b85115a33691766d51ea169f59ad5e939e9ee3b1c288","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"043ea3e75d3dec95b8c0a46ee49c71f885f8e7e77d50ca54c7d00b94839adb53","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"07c73cd15dd5ffaa000f71589f1c38f32d629d45be1705794d5ae3cc0e286a9c","detail":{"divided_from":"body","block":31,"kind":"p"},"prev":"genesis","hash":"043ea3e75d3dec95b8c0a46ee49c71f885f8e7e77d50ca54c7d00b94839adb53"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d31"},{"id":"d32","kind":"p","type":null,"order":32,"text":"See /a/oip-final-testimony for end-to-end ledger requirements.","status":"active","vx_hash":"bdd489a0179650b4830765bee1ef46b53b4d3332b4b9db8fc5d78ae13c98df8b","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"806962a7025c115bee415a6835a394aedd3de053fd4bfb3d26d6eb5cac5397c1","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"ae10cc0cb69b2e6956cd6ade312d7aac175413a5d2aab8834cc9e4bee45c6afd","detail":{"divided_from":"body","block":32,"kind":"p"},"prev":"genesis","hash":"806962a7025c115bee415a6835a394aedd3de053fd4bfb3d26d6eb5cac5397c1"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d32"},{"id":"d33","kind":"h","type":null,"order":33,"text":"## Mechanistic derivation summary","status":"active","vx_hash":"4eb1a6c8aafdab77babcfe79c72e9bc221764fed72fb3855c4dd9f7c1c60bbe0","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"10c6dfc77434c7857ac7f6cffc802853d9fc0cfd73159301246a0955bfbd1bd9","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"842c0c1f469db629378fad2556e0d44018444aa0fa3a9bec9688f98266eaceda","detail":{"divided_from":"body","block":33,"kind":"h"},"prev":"genesis","hash":"10c6dfc77434c7857ac7f6cffc802853d9fc0cfd73159301246a0955bfbd1bd9"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d33"},{"id":"d34","kind":"p","type":null,"order":34,"text":"The renormalization-group equation for the coupling u reads β(u) = −ε u + (n+8) u² / 6 plus higher orders. Setting β(u*) = 0 yields u* proportional to ε. Linearization around u* produces the exponent corrections. Each algebraic step follows from the functional-integral representation of the partition function under momentum-shell integration.","status":"active","vx_hash":"c110ba0a8a3b96a14a86532b6f5a00d9aa0bb2f2bb44a7d1064e515e370f9990","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"64ac6c00ca578df12173cd1b0af2218b44c5a6bb3b58ee106dbbfc1c9e7930f8","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"4d9212975b3c904bc6e3bd3332e2bc449ac481cd4ba3cc2bd7a2dc70f1b725ba","detail":{"divided_from":"body","block":34,"kind":"p"},"prev":"genesis","hash":"64ac6c00ca578df12173cd1b0af2218b44c5a6bb3b58ee106dbbfc1c9e7930f8"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d34"},{"id":"d35","kind":"p","type":null,"order":35,"text":"The derivation is fully reversible within the perturbative regime. Replaying the flow from the fixed point recovers the same exponents.","status":"active","vx_hash":"38cba968a0d776d122a644006aede255d80932319d51e3bc02113f528c5f4b4a","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"1ef52f4123e64dfcdd65e243a32122a83cdc7ecfefcbd7404205ae61f3f4cfb3","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:46.497Z","actor":"owner","text_sha":"4ce10d705ef9a57099d0f37a1fb44075dfb9e6d25652763f2a9a9427a618e855","detail":{"divided_from":"body","block":35,"kind":"p"},"prev":"genesis","hash":"1ef52f4123e64dfcdd65e243a32122a83cdc7ecfefcbd7404205ae61f3f4cfb3"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:46.497Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-wilson-k-g-and-fisher-m-e-1972-critical-exponents-in-3-99-dimensions-physical-re/d35"},{"id":"d36","kind":"p","type":null,"order":36,"text":"Receipt of the result is the published letter itself. Conformance is verified by independent reproduction of the ε coefficients in later 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Hamiltonian is the object; the renormalization transformation is the invocation; the fixed-point values constitute the ledger; the printed exponents are the receipt; replay consists of repeating the momentum-shell integration; repair consists of extending the series to higher orders in 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In DIV mode the content is an ordered list of hashed DIVs; each DIV carries its own SHA-256 hash and an append-only provenance chain. Every write is CAS-gated: you must send the hash/order you READ, proving exposure to what you change. Every successful write returns a clickable human permalink.","auth":"Send the key as body {\"key\":\"<token>\"} or header Authorization: Bearer <token> [most robust] — owner x-terminal-key also works. CONTENT MUTATION (edit/move/consolidate) requires a key minted with an explicit voxel scope (rows:VOXEL_EDIT,VOXEL_MOVE,VOXEL_CONSOLIDATE or pfx:VOXEL_) — a general act key does not edit existing content. Filing a challenge or attestation needs no key at all.","web_runtime":"WEB CHATGPT: open https://miscsubjects.com/api/model-lane first. Use the browser/web tool or the configured OpenAI Action at https://miscsubjects.com/api/openai/actions.json. Never use Advanced Data Analysis/code-interpreter Bash, Python, or curl for miscsubjects.com. 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