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The result looks wild and random yet carries measurable scaling rules.","status":"active","vx_hash":"f5d16f92479545546fb367fca916ea0a96166671066583c1927abe0c6dc1d6a9","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"cdd0828e2cf0d6746f4aaa99ef034ab52a03064df9fc6f15cb84c07d0a8a19f7","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"f006dac384c552e89c826c892256f1dbf932bb27b2fc289f6aedc25ac49d83c4","detail":{"divided_from":"body","block":7,"kind":"p"},"prev":"genesis","hash":"cdd0828e2cf0d6746f4aaa99ef034ab52a03064df9fc6f15cb84c07d0a8a19f7"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d7"},{"id":"d8","kind":"p","type":null,"order":8,"text":"No page-specific verbatim excerpts from the 1997 volume appear in public previews examined. All claims below rest on book descriptions and author summaries of its contents.","status":"active","vx_hash":"a1d5409a994fb20a4cbb670ba30d4a1a920e17525bcb56b8700e676dd060a4e2","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"8738719ead45b19bb36574671c64d2cb5e83d21c940aa97211d62c639b03eb9a","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"dac04202230350ad9135b88eddd9f47c6688e3e37fc656540a7cbaf0d5b2804f","detail":{"divided_from":"body","block":8,"kind":"p"},"prev":"genesis","hash":"8738719ead45b19bb36574671c64d2cb5e83d21c940aa97211d62c639b03eb9a"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d8"},{"id":"d9","kind":"h","type":null,"order":9,"text":"## Convergence patterns the work touches","status":"active","vx_hash":"8b05c086be7743dfca8c03aabd8e1f6b507059c7d753ff7fab04c5c936eca886","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"92edea919aa300e4c7cbfdd86e15d6df36e0424fa8049875d158a688ac72188c","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"b6d9d72e19d6be3f78a04abcf3c3cfe506c7689994f1b7454a69a2a2de2e7f44","detail":{"divided_from":"body","block":9,"kind":"h"},"prev":"genesis","hash":"92edea919aa300e4c7cbfdd86e15d6df36e0424fa8049875d158a688ac72188c"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d9"},{"id":"d10","kind":"p","type":null,"order":10,"text":"The book evidences scale invariance. Price statistics repeat at daily, weekly, and monthly horizons.","status":"active","vx_hash":"c994cb78935678281cd04a98d43fc7770cf1e4cc0af8fca4954df32418714329","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"f5fad180d33e264cd4a6040a35ab2fabd4a40741921ec11525ebd15e21aca614","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"a399c3dae171b11c760426714eb2a0a4ff9bc70feb988eb4b58a7cc49fa22f01","detail":{"divided_from":"body","block":10,"kind":"p"},"prev":"genesis","hash":"f5fad180d33e264cd4a6040a35ab2fabd4a40741921ec11525ebd15e21aca614"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d10"},{"id":"d11","kind":"p","type":null,"order":11,"text":"It evidences bounded chaos. Price paths wander far yet stay within measurable roughness bounds set by the multifractal spectrum.","status":"active","vx_hash":"1dfa248259f042516d02e282dd50dfaf725de04262ed91378837ab83432452e7","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"fa244c1b4916d35edb745a0e44338d1d94a4b78e32577186ce81ed448988a550","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"f814dd2392cf2a7288109f461e4a913f003f88cefe1b389bcab5c0d048b537d5","detail":{"divided_from":"body","block":11,"kind":"p"},"prev":"genesis","hash":"fa244c1b4916d35edb745a0e44338d1d94a4b78e32577186ce81ed448988a550"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d11"},{"id":"d12","kind":"p","type":null,"order":12,"text":"It evidences memory. Dependence persists across lags longer than standard models allow.","status":"active","vx_hash":"40712f4ca5a0306025d6265b5f464296aa266bd5aa7bcfb3e636a04b71c471e1","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"87ab6b58216f6d64de5daea9127c06fa9000b6ed4227f2f007b490419b8a6272","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"ac5f0ae7dd02573eae528b8a84593d5de9d374ad2bad267eaf3f9319ecc5c83f","detail":{"divided_from":"body","block":12,"kind":"p"},"prev":"genesis","hash":"87ab6b58216f6d64de5daea9127c06fa9000b6ed4227f2f007b490419b8a6272"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d12"},{"id":"d13","kind":"p","type":null,"order":13,"text":"These patterns match the GRAIN list of recurring structural forms: scale invariance, bounded chaos, memory in flow networks.","status":"active","vx_hash":"8492e30e71b01c7af09756e8015f19a74ee9494f28bef2423e872b7cbd6869df","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"4d65152c6c70c8906038fe2d70f85f9d0d8baafd7323fb8d5c3db479cbebc770","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"e69763031eba9c4368f1e21fc1dbf314b402e089063c0f736215fede0f4e811a","detail":{"divided_from":"body","block":13,"kind":"p"},"prev":"genesis","hash":"4d65152c6c70c8906038fe2d70f85f9d0d8baafd7323fb8d5c3db479cbebc770"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d13"},{"id":"d14","kind":"h","type":null,"order":14,"text":"## Distance from the full OIP/GRAIN synthesis","status":"active","vx_hash":"9ec73c923683b418cb959ad252d03cd05021736b551381bd1b201b5fb7ddde63","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"08fa5a76df93d35cb551cb80b840f1ea2be2a4c1e69aac2740ea94850afac05e","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"78b248fc09f46aa233e0ee4e7ccd8141328a45bdb7ef545daf36dd82e28468ad","detail":{"divided_from":"body","block":14,"kind":"h"},"prev":"genesis","hash":"08fa5a76df93d35cb551cb80b840f1ea2be2a4c1e69aac2740ea94850afac05e"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d14"},{"id":"d15","kind":"p","type":null,"order":15,"text":"The work stays inside economic price series. It stops at statistical description of discontinuity and 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difference to flow to structure to memory to life to mind.","status":"active","vx_hash":"e90d32fe30add65ebb2812a8b1c908c7f0b084cbe047be7882fb288649b9bdb1","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"424115944af56c6effa8b46ead0fc82ee0ea5c5f72f6595a680e1d7fab87f141","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"0433056af3fe779eed30e49bcff6b7dbc16aabff9d8247a4e6fd24ae4ccce6fe","detail":{"divided_from":"body","block":16,"kind":"p"},"prev":"genesis","hash":"424115944af56c6effa8b46ead0fc82ee0ea5c5f72f6595a680e1d7fab87f141"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d16"},{"id":"d17","kind":"p","type":null,"order":17,"text":"It supplies no Mirror Layer statement that the observer sits inside the measured 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series yet offer no guarantee of future performance. Markets can shift regimes.","status":"active","vx_hash":"49e6167c4a627c46b1eeb30986b630c6ed8df019cc78ac586a7483d426bd4d51","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"9c71988d8366d33858dcef7397b599e474db1795aa330d6d66317d9fc3853c0b","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"6bcb566fe9d5350d02d052b8978a00c9474487fa4e323f44bb3561767f206570","detail":{"divided_from":"body","block":20,"kind":"p"},"prev":"genesis","hash":"9c71988d8366d33858dcef7397b599e474db1795aa330d6d66317d9fc3853c0b"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d20"},{"id":"d21","kind":"p","type":null,"order":21,"text":"The mathematics is mechanistic and formally developed inside the book. Empirical tests on new data sets can still falsify specific parameter choices.","status":"active","vx_hash":"6ba4dcf7cdb7bc2d38cb76abff91503bf7f556539f883291b3cb1d25c0dc3c28","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"a2d52f2c6d5b3b57e243f137b2ac17ee453f99c7e4f1c37a4fc5f92545890315","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"8af047de68fe43816a6517b21ae772bcb891a5cce7b60ea24a1dea849fe4f641","detail":{"divided_from":"body","block":21,"kind":"p"},"prev":"genesis","hash":"a2d52f2c6d5b3b57e243f137b2ac17ee453f99c7e4f1c37a4fc5f92545890315"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d21"},{"id":"d22","kind":"p","type":null,"order":22,"text":"Reductionist critics note that the approach adds parameters. They ask whether simpler models plus occasional jumps suffice for most practical risk calculations.","status":"active","vx_hash":"2701d99f82baeacc1b04d2fecb11d49ab42985c77bde4e06170c3f7cda4df875","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"e7d90f6fd597c71a6c5051a0964b51d5fe6955d7f42fe915e879ffe808f7c5a2","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"e8e203af00b71915f821a0f2ff95aee5f4bf3f5540c9a4794c0225313fc13247","detail":{"divided_from":"body","block":22,"kind":"p"},"prev":"genesis","hash":"e7d90f6fd597c71a6c5051a0964b51d5fe6955d7f42fe915e879ffe808f7c5a2"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d22"},{"id":"d23","kind":"p","type":null,"order":23,"text":"The 1997 volume contains no biological data and no claims about mind or consciousness. 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evidence for one listed convergence pattern.","status":"active","vx_hash":"9b784040e1807e6fb01182b7ee02ba6741aa22964e36957b68a41033568281cd","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"806dbe4399751f5bd41f65647443d5412b42ec5cea40098dd989335bfe9447e8","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"2ff5c639e960198f2cb6c57d0e88acdd8e8f324504061937c922a35a0281980c","detail":{"divided_from":"body","block":25,"kind":"p"},"prev":"genesis","hash":"806dbe4399751f5bd41f65647443d5412b42ec5cea40098dd989335bfe9447e8"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d25"},{"id":"d26","kind":"p","type":null,"order":26,"text":"Multifractal time 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extreme moves occur yet overall roughness remains describable by a finite set of scaling exponents.","status":"active","vx_hash":"25ad5330d121629ad6301bc2ccf073bd2fdd43e644763b991fc9bd99e891f65b","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"c91d96ec932bedd4109108c0449fae18b6c1048467437e951f7e68f5a4734be1","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"3fcdb51905f6e578ad0d86cf14032af540b82b0a7b2270dfebca62ada66e3bbd","detail":{"divided_from":"body","block":27,"kind":"p"},"prev":"genesis","hash":"c91d96ec932bedd4109108c0449fae18b6c1048467437e951f7e68f5a4734be1"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d27"},{"id":"d28","kind":"h","type":null,"order":28,"text":"## Claims that survive examination","status":"active","vx_hash":"669a0ad714083e2d03628ac2ab5fc1d852e05989314999e1da4719a4259e939c","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"02ca8546539c2ae5814b378eed1f61ac64fa445ee575fd962b0b4c72f141533a","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"fd002affaa35470b723641332d9a0a49e80132462336a151ca1b42cdbbf6de90","detail":{"divided_from":"body","block":28,"kind":"h"},"prev":"genesis","hash":"02ca8546539c2ae5814b378eed1f61ac64fa445ee575fd962b0b4c72f141533a"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d28"},{"id":"d29","kind":"p","type":null,"order":29,"text":"Claim: price changes exhibit long-range dependence. Tier: mechanistic. Source: book models and author descriptions.","status":"active","vx_hash":"bb380f39295805a5153e59e0a4f7f25fa233fd156eba5cb41e34e2128e3dd50e","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"9c826c6735acb0286de45a50f5ec8ea8084a2bfd0a8439723f1f38e0e18e7a42","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"88b3e083a5b510347b590d91bbda0ff136f239d1788ab4eb85978ff6571619a4","detail":{"divided_from":"body","block":29,"kind":"p"},"prev":"genesis","hash":"9c826c6735acb0286de45a50f5ec8ea8084a2bfd0a8439723f1f38e0e18e7a42"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d29"},{"id":"d30","kind":"p","type":null,"order":30,"text":"Claim: risk concentrates in a small fraction of trading intervals. Tier: mechanistic. Source: book analysis of concentration.","status":"active","vx_hash":"128c103e3bdd01985eee31da981bfc3fba7f969d3a8b741704a53a50cee17516","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"65e280ca4c8bee06a5ea96217a00b1e10401f27e128299f25eb8fc6461629104","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"dbab0635e26996f31865311c8b4521658761a6446f8a556edb0983f0067067ad","detail":{"divided_from":"body","block":30,"kind":"p"},"prev":"genesis","hash":"65e280ca4c8bee06a5ea96217a00b1e10401f27e128299f25eb8fc6461629104"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d30"},{"id":"d31","kind":"p","type":null,"order":31,"text":"Claim: standard Brownian motion fails to capture observed clustering of volatility. Tier: mechanistic. Source: contrast drawn in the work.","status":"active","vx_hash":"f28b3de1a8a9838ef323f1714d4550d3890ab9d0cfb90b975a5a2a7a83bf9243","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"06ffc01e53d0d34d65c34131748d16f74cd457c27ee87766911c342ed949800c","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"5b3a582ee647d97fdf126e1a9d5aaf01c7e380684f86f6e75fadf993bdf4f967","detail":{"divided_from":"body","block":31,"kind":"p"},"prev":"genesis","hash":"06ffc01e53d0d34d65c34131748d16f74cd457c27ee87766911c342ed949800c"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d31"},{"id":"d32","kind":"p","type":null,"order":32,"text":"All other statements about broader synthesis remain extensions by later readers.","status":"active","vx_hash":"bc0a4bb30964df4676d35b4b824b493014cf844cea3e6f00b9e877f9885e8147","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"ea8c52c65235088e8e6fa6d75b5e6ee4ccd520a83416d6c302f90d1558bee60c","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"e067e24a4bfbc23f71cc4ff43ee4a780d720a85c491ae53f3a450a645888ace2","detail":{"divided_from":"body","block":32,"kind":"p"},"prev":"genesis","hash":"ea8c52c65235088e8e6fa6d75b5e6ee4ccd520a83416d6c302f90d1558bee60c"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d32"},{"id":"d33","kind":"h","type":null,"order":33,"text":"## End-to-end example inside finance data","status":"active","vx_hash":"47cc92956e3d10b2e6affe56459add008a3110597081b10b8980556cf1084b12","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"2f5a38009536dd65d3d741f5a7cea38bb44add57e9b8ce2c08f6b402b8ac2b25","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"49a6312c0511a9fc3517da27dba23f18795823667d3f4c81aef53389bec25ac0","detail":{"divided_from":"body","block":33,"kind":"h"},"prev":"genesis","hash":"2f5a38009536dd65d3d741f5a7cea38bb44add57e9b8ce2c08f6b402b8ac2b25"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d33"},{"id":"d34","kind":"p","type":null,"order":34,"text":"Take daily closes of a major index over decades. Compute the distribution of returns at 1-day, 5-day, and 20-day horizons. The tails remain heavier than Gaussian at every horizon. The degree of heaviness scales according to a multifractal spectrum. Quiet decades and turbulent decades both fit the same family of curves after time is rescaled.","status":"active","vx_hash":"43f3138cf5d20f5656b87696acb4a8d814cca84ef6c07dfa8ac095dacccd0fc7","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"fa966dcd3abbb7d71ac6c7f64b0e9bfb7675f55fa0cc52a4607477a5ef93d450","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"08b91507d16c0b473a712f9739e8bb0cab36b612f8cacc55e07b04625f4eed24","detail":{"divided_from":"body","block":34,"kind":"p"},"prev":"genesis","hash":"fa966dcd3abbb7d71ac6c7f64b0e9bfb7675f55fa0cc52a4607477a5ef93d450"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d34"},{"id":"d35","kind":"h","type":null,"order":35,"text":"## Receipt rule for the pattern","status":"active","vx_hash":"9409d7979ee821c98f91c12b4a9441a3afad591cf7f807522f6ad9715dc9b298","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"02fad231272919cd3607d0a014457ec8c0f8fb907e5bfa0b670d05c6f7fe9616","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"249bc74f37984f97b6a148af33284b12b2be024bae3780e0746e97335f60bcbf","detail":{"divided_from":"body","block":35,"kind":"h"},"prev":"genesis","hash":"02fad231272919cd3607d0a014457ec8c0f8fb907e5bfa0b670d05c6f7fe9616"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d35"},{"id":"d36","kind":"p","type":null,"order":36,"text":"Any replication study that recomputes the multifractal spectrum on an independent price series and recovers the same scaling exponents counts as a receipt. The receipt must state the data source, the exact spectrum parameters, and the goodness-of-fit measure.","status":"active","vx_hash":"9e5014784f17fa364d97722d8a196f35babc84d67912bfb55b6450de818237fe","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"6ad0a080d1a79f0e1dd5cfcec96815b45b59cc68721a6d32f8608e92e1926c35","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"7b82aeaa5fb5efe5727a9144329d7528b5166f816014524f955ac453a6cc5612","detail":{"divided_from":"body","block":36,"kind":"p"},"prev":"genesis","hash":"6ad0a080d1a79f0e1dd5cfcec96815b45b59cc68721a6d32f8608e92e1926c35"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d36"},{"id":"d37","kind":"h","type":null,"order":37,"text":"## Conformance rule","status":"active","vx_hash":"c9f79751f66fdeeba495b9784607943d6916f26a50826b6c4f4e5c0a0f16b003","semantic_hash":null,"version_hash":null,"version":1,"sources":[],"falsifiers":[],"tier":null,"backed":null,"transcludes":null,"chain_head":"d3825030380f4aa90be209aa791b975247fcc4fbfccc8fd5f554d6dbe0672d36","chain_length":1,"chain":[{"n":1,"op":"genesis","ts":"2026-07-17T02:37:20.691Z","actor":"owner","text_sha":"c994c8ce87fede78e7e014cd5bd13bbce8dc47a94cdd32c7c8406caae4c90737","detail":{"divided_from":"body","block":37,"kind":"h"},"prev":"genesis","hash":"d3825030380f4aa90be209aa791b975247fcc4fbfccc8fd5f554d6dbe0672d36"}],"claim_ids":[],"last_op":{"op":"genesis","actor":"owner","ts":"2026-07-17T02:37:20.691Z"},"consolidated_into":null,"stable_url":"https://miscsubjects.com/i/div/paper-mandelbrot-b-b-1997-fractals-and-scaling-in-finance-discontinuity-concentration/d37"},{"id":"d38","kind":"p","type":null,"order":38,"text":"A later model conforms when it reproduces the three documented features: discontinuity, concentration, and scaling across horizons. Models that assume continuous paths or finite variance fail conformance on these data 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long-range dependence and clustering of volatility.","tier":"mechanistic","standing":null,"weight":0.3,"section":"Core results","status":"active","source_ids":["s1"],"source_status":"sourced","posted_by":{"actor":"grok/grok-4.3","channel":"protocol/draft","ts":"2026-07-09T23:40:53-07:00","model":"grok/grok-4.3","rationale":""},"who_claims":"grok/grok-4.3","edges":[{"type":"supported_by","target":"s1","source_type":"other","hash":"1877372747936f40"},{"type":"posted_by","actor":"grok/grok-4.3","channel":"protocol/draft","ts":"2026-07-09T23:40:53-07:00"}],"why_material":"Directly supports scale invariance and memory in flow 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