{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:J4U37VRT526QL3WZVQYR4FQX6O","short_pith_number":"pith:J4U37VRT","canonical_record":{"source":{"id":"2607.04505","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-07-05T21:16:31Z","cross_cats_sorted":[],"title_canon_sha256":"c64edefb72f46b550bef17253727e549b45270c01bc505f8c7cff3e06f4a3ba8","abstract_canon_sha256":"a903af23d942d55bfd289d7925f0646686b16180e9c97d915897fd6adf8e835f"},"schema_version":"1.0"},"canonical_sha256":"4f29bfd633eebd05eed9ac311e1617f3951b9c9ee7622d0df36719ff03772183","source":{"kind":"arxiv","id":"2607.04505","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04505","created_at":"2026-07-07T02:19:22Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04505v1","created_at":"2026-07-07T02:19:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04505","created_at":"2026-07-07T02:19:22Z"},{"alias_kind":"pith_short_12","alias_value":"J4U37VRT526Q","created_at":"2026-07-07T02:19:22Z"},{"alias_kind":"pith_short_16","alias_value":"J4U37VRT526QL3WZ","created_at":"2026-07-07T02:19:22Z"},{"alias_kind":"pith_short_8","alias_value":"J4U37VRT","created_at":"2026-07-07T02:19:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:J4U37VRT526QL3WZVQYR4FQX6O","target":"record","payload":{"canonical_record":{"source":{"id":"2607.04505","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-07-05T21:16:31Z","cross_cats_sorted":[],"title_canon_sha256":"c64edefb72f46b550bef17253727e549b45270c01bc505f8c7cff3e06f4a3ba8","abstract_canon_sha256":"a903af23d942d55bfd289d7925f0646686b16180e9c97d915897fd6adf8e835f"},"schema_version":"1.0"},"canonical_sha256":"4f29bfd633eebd05eed9ac311e1617f3951b9c9ee7622d0df36719ff03772183","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:19:22.461686Z","signature_b64":"TgRI5BgfTFIL3hTLcDtRTjamrwf3RY76KHEtW3N249iAUQhV8FEub+n9atxPDNpu/8IvgJJw4f/B3k9xs7QyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f29bfd633eebd05eed9ac311e1617f3951b9c9ee7622d0df36719ff03772183","last_reissued_at":"2026-07-07T02:19:22.461015Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:19:22.461015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.04505","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-07T02:19:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lR42/U1k2wFx6A3GmHSx+5jswkqDFiaIwthbCvLEpPkV0AzOmdSYSsJKbndDOISkKv0GUg5q4NFStCfFxyxrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T20:42:16.634110Z"},"content_sha256":"404b9b57775b366a33fd8c2ed2fa2d3810239a09e191a67d9128862759f56139","schema_version":"1.0","event_id":"sha256:404b9b57775b366a33fd8c2ed2fa2d3810239a09e191a67d9128862759f56139"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:J4U37VRT526QL3WZVQYR4FQX6O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Charanjit S. Jutla, Vimal Sharma","submitted_at":"2026-07-05T21:16:31Z","abstract_excerpt":"We advance the hypothesis that human mathematical reasoning, constrained by both the undecidability and the computational intractability of even modest logical fragments, relies fundamentally on pattern matching from domains external to pure deduction. The most prolific reservoir of such patterns is the natural world, whose physical laws and biological systems have undergone billions of years of ``pre-computation'' and already exhibit surprisingly innovative solutions. To ground this claim, we trace the history of the Fourier transform and relevant mathematics, from the vibrating string contro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04505","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.04505/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-07T02:19:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IHsxZmb3/nLWUqjicZbNotpu5nSMvzgkLPmEN8tHEtGuFBoHUsBJduiiM2p9bxwKbRYrAJBSrvfV1g7i1NUMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T20:42:16.634670Z"},"content_sha256":"fbd13e39a0a6aab7c095d1b8b2509475aa82ee0be8be8dd855d5b5b4412abd5e","schema_version":"1.0","event_id":"sha256:fbd13e39a0a6aab7c095d1b8b2509475aa82ee0be8be8dd855d5b5b4412abd5e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J4U37VRT526QL3WZVQYR4FQX6O/bundle.json","state_url":"https://pith.science/pith/J4U37VRT526QL3WZVQYR4FQX6O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J4U37VRT526QL3WZVQYR4FQX6O/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-02T20:42:16Z","links":{"resolver":"https://pith.science/pith/J4U37VRT526QL3WZVQYR4FQX6O","bundle":"https://pith.science/pith/J4U37VRT526QL3WZVQYR4FQX6O/bundle.json","state":"https://pith.science/pith/J4U37VRT526QL3WZVQYR4FQX6O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J4U37VRT526QL3WZVQYR4FQX6O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:J4U37VRT526QL3WZVQYR4FQX6O","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a903af23d942d55bfd289d7925f0646686b16180e9c97d915897fd6adf8e835f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-07-05T21:16:31Z","title_canon_sha256":"c64edefb72f46b550bef17253727e549b45270c01bc505f8c7cff3e06f4a3ba8"},"schema_version":"1.0","source":{"id":"2607.04505","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04505","created_at":"2026-07-07T02:19:22Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04505v1","created_at":"2026-07-07T02:19:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04505","created_at":"2026-07-07T02:19:22Z"},{"alias_kind":"pith_short_12","alias_value":"J4U37VRT526Q","created_at":"2026-07-07T02:19:22Z"},{"alias_kind":"pith_short_16","alias_value":"J4U37VRT526QL3WZ","created_at":"2026-07-07T02:19:22Z"},{"alias_kind":"pith_short_8","alias_value":"J4U37VRT","created_at":"2026-07-07T02:19:22Z"}],"graph_snapshots":[{"event_id":"sha256:fbd13e39a0a6aab7c095d1b8b2509475aa82ee0be8be8dd855d5b5b4412abd5e","target":"graph","created_at":"2026-07-07T02:19:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.04505/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We advance the hypothesis that human mathematical reasoning, constrained by both the undecidability and the computational intractability of even modest logical fragments, relies fundamentally on pattern matching from domains external to pure deduction. The most prolific reservoir of such patterns is the natural world, whose physical laws and biological systems have undergone billions of years of ``pre-computation'' and already exhibit surprisingly innovative solutions. To ground this claim, we trace the history of the Fourier transform and relevant mathematics, from the vibrating string contro","authors_text":"Charanjit S. Jutla, Vimal Sharma","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-07-05T21:16:31Z","title":"Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04505","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:404b9b57775b366a33fd8c2ed2fa2d3810239a09e191a67d9128862759f56139","target":"record","created_at":"2026-07-07T02:19:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a903af23d942d55bfd289d7925f0646686b16180e9c97d915897fd6adf8e835f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-07-05T21:16:31Z","title_canon_sha256":"c64edefb72f46b550bef17253727e549b45270c01bc505f8c7cff3e06f4a3ba8"},"schema_version":"1.0","source":{"id":"2607.04505","kind":"arxiv","version":1}},"canonical_sha256":"4f29bfd633eebd05eed9ac311e1617f3951b9c9ee7622d0df36719ff03772183","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f29bfd633eebd05eed9ac311e1617f3951b9c9ee7622d0df36719ff03772183","first_computed_at":"2026-07-07T02:19:22.461015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:19:22.461015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TgRI5BgfTFIL3hTLcDtRTjamrwf3RY76KHEtW3N249iAUQhV8FEub+n9atxPDNpu/8IvgJJw4f/B3k9xs7QyAQ==","signature_status":"signed_v1","signed_at":"2026-07-07T02:19:22.461686Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.04505","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:404b9b57775b366a33fd8c2ed2fa2d3810239a09e191a67d9128862759f56139","sha256:fbd13e39a0a6aab7c095d1b8b2509475aa82ee0be8be8dd855d5b5b4412abd5e"],"state_sha256":"f2685c050eee4043c00e40ed0ba362ade4268d5389d2ea540ef45e8b03cb2ee6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b9tbsdhiH1LNpm9lFUuuNB8XdktU4RkiArdzRQ3u+XKs+Dkbbnc0Ba7wXqZ/JIzJmjHpihbANxEJcGnWbufhCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-02T20:42:16.638912Z","bundle_sha256":"60235ecdca7bbe049bccc1c97d7b5a0e744f8710a8da272f52634906cc349678"}}