{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WQTEGSMYLKMD4W5JO3735S47VL","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":"47cfa1c5f201b3263156ef49c8e0baf8f8731d4ef329df614b436f9ff3d663da","cross_cats_sorted":["physics.pop-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2015-04-25T06:12:24Z","title_canon_sha256":"16e1ee9ac944d761dc3b4b358ed3c88bea474fc25337decc7c3ccd23f7c9de27"},"schema_version":"1.0","source":{"id":"1504.06686","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06686","created_at":"2026-05-18T01:34:34Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06686v2","created_at":"2026-05-18T01:34:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06686","created_at":"2026-05-18T01:34:34Z"},{"alias_kind":"pith_short_12","alias_value":"WQTEGSMYLKMD","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WQTEGSMYLKMD4W5J","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WQTEGSMY","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:0b28e77ccce0814385f38f6f0d51df148b974b2bbf6c390a0cddf605840e5292","target":"graph","created_at":"2026-05-18T01:34:34Z","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"},"paper":{"abstract_excerpt":"Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as exemplified by the laws of physics. In this essay, I claim that much of the utility of mathematics arises from our choice of description of the physical world coupled with our desire to quantify it. This will be demonstrated in a practical sense by considering one of the most fundamental concepts of mathematics: additivity. This example will be used to show how many ","authors_text":"Kevin H. Knuth","cross_cats":["physics.pop-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2015-04-25T06:12:24Z","title":"The Deeper Roles of Mathematics in Physical Laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06686","kind":"arxiv","version":2},"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:e3fed1400c20fd28f4ca732d44daba5a47895a0644ebf8956ec629c9b026dca4","target":"record","created_at":"2026-05-18T01:34:34Z","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":"47cfa1c5f201b3263156ef49c8e0baf8f8731d4ef329df614b436f9ff3d663da","cross_cats_sorted":["physics.pop-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2015-04-25T06:12:24Z","title_canon_sha256":"16e1ee9ac944d761dc3b4b358ed3c88bea474fc25337decc7c3ccd23f7c9de27"},"schema_version":"1.0","source":{"id":"1504.06686","kind":"arxiv","version":2}},"canonical_sha256":"b4264349985a983e5ba976ffbecb9faadf73381b3f99cd5580c399a6d5fdc648","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4264349985a983e5ba976ffbecb9faadf73381b3f99cd5580c399a6d5fdc648","first_computed_at":"2026-05-18T01:34:34.777433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:34.777433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UC0rH1/cmCVHBhTosqspw6XoUN39L4QDZK1ICOTnSGldFiX8X+82sXgFX4rvBWB46bFkz6cJgiWd8/5zOu5jBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:34.778087Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06686","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3fed1400c20fd28f4ca732d44daba5a47895a0644ebf8956ec629c9b026dca4","sha256:0b28e77ccce0814385f38f6f0d51df148b974b2bbf6c390a0cddf605840e5292"],"state_sha256":"be931a9b604e56b5bc52b1aea6f900cb92632068b7c1d09325301d92ee4303b2"}