{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4QXQOCVSQQ75D6C2P3DAHU5T7W","short_pith_number":"pith:4QXQOCVS","schema_version":"1.0","canonical_sha256":"e42f070ab2843fd1f85a7ec603d3b3fda3350ddd35fd18fb7c1b884c54173783","source":{"kind":"arxiv","id":"1505.05859","version":7},"attestation_state":"computed","paper":{"title":"Path algebras, wave-particle duality, and quantization of phase space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.RA","authors_text":"Murray Gerstenhaber","submitted_at":"2015-05-21T19:51:49Z","abstract_excerpt":"Semigroup algebras admit certain `coherent' deformations which, in the special case of a path algebra, may associate a periodic function to an evolving path; for a particle moving freely on a straight line after an initial impulse, the wave length is that hypothesized by de Broglie's wave-particle duality. This theory leads to a model of \"physical\" phase space of which mathematical phase space, the cotangent bundle of configuration space, is a projection. This space is singular, quantized at the Planck level, its structure implies the existence of spin, and the spread of a packet can be descri"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1505.05859","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-05-21T19:51:49Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"e1932f7b89a38d12ba775b9c0e2c72c759495a90fd044300e0676ab7ad583b5a","abstract_canon_sha256":"44dbbfbb0567ffb13886ca3463f1a189fde2bb46cc7c41acacc568d9e5bae38f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:41.619822Z","signature_b64":"uUex91XE9BvueJgjiE9VlyHYw5L6F3lH6jGVEa4aa5RIocEl4n7tx3YaEovCI1JDP/yiI5X4meId0a73802LBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e42f070ab2843fd1f85a7ec603d3b3fda3350ddd35fd18fb7c1b884c54173783","last_reissued_at":"2026-05-18T00:54:41.619424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:41.619424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Path algebras, wave-particle duality, and quantization of phase space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.RA","authors_text":"Murray Gerstenhaber","submitted_at":"2015-05-21T19:51:49Z","abstract_excerpt":"Semigroup algebras admit certain `coherent' deformations which, in the special case of a path algebra, may associate a periodic function to an evolving path; for a particle moving freely on a straight line after an initial impulse, the wave length is that hypothesized by de Broglie's wave-particle duality. This theory leads to a model of \"physical\" phase space of which mathematical phase space, the cotangent bundle of configuration space, is a projection. This space is singular, quantized at the Planck level, its structure implies the existence of spin, and the spread of a packet can be descri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05859","kind":"arxiv","version":7},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1505.05859","created_at":"2026-05-18T00:54:41.619487+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.05859v7","created_at":"2026-05-18T00:54:41.619487+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05859","created_at":"2026-05-18T00:54:41.619487+00:00"},{"alias_kind":"pith_short_12","alias_value":"4QXQOCVSQQ75","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4QXQOCVSQQ75D6C2","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4QXQOCVS","created_at":"2026-05-18T12:29:05.191682+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4QXQOCVSQQ75D6C2P3DAHU5T7W","json":"https://pith.science/pith/4QXQOCVSQQ75D6C2P3DAHU5T7W.json","graph_json":"https://pith.science/api/pith-number/4QXQOCVSQQ75D6C2P3DAHU5T7W/graph.json","events_json":"https://pith.science/api/pith-number/4QXQOCVSQQ75D6C2P3DAHU5T7W/events.json","paper":"https://pith.science/paper/4QXQOCVS"},"agent_actions":{"view_html":"https://pith.science/pith/4QXQOCVSQQ75D6C2P3DAHU5T7W","download_json":"https://pith.science/pith/4QXQOCVSQQ75D6C2P3DAHU5T7W.json","view_paper":"https://pith.science/paper/4QXQOCVS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.05859&json=true","fetch_graph":"https://pith.science/api/pith-number/4QXQOCVSQQ75D6C2P3DAHU5T7W/graph.json","fetch_events":"https://pith.science/api/pith-number/4QXQOCVSQQ75D6C2P3DAHU5T7W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4QXQOCVSQQ75D6C2P3DAHU5T7W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4QXQOCVSQQ75D6C2P3DAHU5T7W/action/storage_attestation","attest_author":"https://pith.science/pith/4QXQOCVSQQ75D6C2P3DAHU5T7W/action/author_attestation","sign_citation":"https://pith.science/pith/4QXQOCVSQQ75D6C2P3DAHU5T7W/action/citation_signature","submit_replication":"https://pith.science/pith/4QXQOCVSQQ75D6C2P3DAHU5T7W/action/replication_record"}},"created_at":"2026-05-18T00:54:41.619487+00:00","updated_at":"2026-05-18T00:54:41.619487+00:00"}