{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5OFZP4D5LPKSAUB3O5ABSBFAJF","short_pith_number":"pith:5OFZP4D5","canonical_record":{"source":{"id":"2409.11866","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-09-18T10:44:23Z","cross_cats_sorted":["gr-qc","math-ph","math.MP","quant-ph"],"title_canon_sha256":"27d92e8d58f90f830386292f91cebee9404993f3d5eeed78c7ee1767da0d6954","abstract_canon_sha256":"c1efa5c118a229949e4cf12f3c4b0bfe60ffa91fc60db429f3c2fe647ad86234"},"schema_version":"1.0"},"canonical_sha256":"eb8b97f07d5bd520503b77401904a0496e2c3916799ab60f8dfa55a8d8430382","source":{"kind":"arxiv","id":"2409.11866","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.11866","created_at":"2026-07-05T10:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"2409.11866v2","created_at":"2026-07-05T10:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.11866","created_at":"2026-07-05T10:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"5OFZP4D5LPKS","created_at":"2026-07-05T10:28:21Z"},{"alias_kind":"pith_short_16","alias_value":"5OFZP4D5LPKSAUB3","created_at":"2026-07-05T10:28:21Z"},{"alias_kind":"pith_short_8","alias_value":"5OFZP4D5","created_at":"2026-07-05T10:28:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5OFZP4D5LPKSAUB3O5ABSBFAJF","target":"record","payload":{"canonical_record":{"source":{"id":"2409.11866","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-09-18T10:44:23Z","cross_cats_sorted":["gr-qc","math-ph","math.MP","quant-ph"],"title_canon_sha256":"27d92e8d58f90f830386292f91cebee9404993f3d5eeed78c7ee1767da0d6954","abstract_canon_sha256":"c1efa5c118a229949e4cf12f3c4b0bfe60ffa91fc60db429f3c2fe647ad86234"},"schema_version":"1.0"},"canonical_sha256":"eb8b97f07d5bd520503b77401904a0496e2c3916799ab60f8dfa55a8d8430382","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:28:21.883021Z","signature_b64":"ef8fZoUz/0EKqRwesGW+vTocE9PXkvvQ0CIuRoMDEW5xn2nNg8epGG2mcqha+SibIN5riWj8XHZ0J1OFL43XCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb8b97f07d5bd520503b77401904a0496e2c3916799ab60f8dfa55a8d8430382","last_reissued_at":"2026-07-05T10:28:21.882585Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:28:21.882585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.11866","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:28:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hPXFTNVWzjTsSVZlVVAHEgOoSDs5azeDCMd60DFkUOwC2ePY3c1GSNfm0cWPPbQKfngc9Dm4BJYYYDFYS51TAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T21:24:09.742026Z"},"content_sha256":"69a0a0af6d9c2790158c2c221e98bb86168d8a7a621d1d30951891f37738291b","schema_version":"1.0","event_id":"sha256:69a0a0af6d9c2790158c2c221e98bb86168d8a7a621d1d30951891f37738291b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5OFZP4D5LPKSAUB3O5ABSBFAJF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Stochastic Origin of Spacetime Non-Commutativity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"Folkert Kuipers, Michele Arzano","submitted_at":"2024-09-18T10:44:23Z","abstract_excerpt":"We propose a stochastic interpretation of spacetime non-commutativity starting from the path integral formulation of quantum mechanical commutation relations. We discuss how the (non-)commutativity of spacetime is inherently related to the continuity or discontinuity of paths in the path integral formulation. Utilizing Wiener processes, we demonstrate that continuous paths lead to commutative spacetime, whereas discontinuous paths correspond to non-commutative spacetime structures. As an example we introduce discontinuous paths from which the $\\kappa$-Minkowski spacetime commutators can be obt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.11866","kind":"arxiv","version":2},"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/2409.11866/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":"2026-07-05T10:28:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FP8j0ikH10FPJrtZwmzidQy4mgImKFX4eUEWS+AILau1KGlJlE1Qzz8qOAd3GkGQa4alU+mLJ/MUSOdc7owYBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T21:24:09.742674Z"},"content_sha256":"28e72889e13b40d76d5ef4ebfe61d7a785089455957142516b819daa37eb167d","schema_version":"1.0","event_id":"sha256:28e72889e13b40d76d5ef4ebfe61d7a785089455957142516b819daa37eb167d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5OFZP4D5LPKSAUB3O5ABSBFAJF/bundle.json","state_url":"https://pith.science/pith/5OFZP4D5LPKSAUB3O5ABSBFAJF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5OFZP4D5LPKSAUB3O5ABSBFAJF/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":"2026-08-16T21:24:09Z","links":{"resolver":"https://pith.science/pith/5OFZP4D5LPKSAUB3O5ABSBFAJF","bundle":"https://pith.science/pith/5OFZP4D5LPKSAUB3O5ABSBFAJF/bundle.json","state":"https://pith.science/pith/5OFZP4D5LPKSAUB3O5ABSBFAJF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5OFZP4D5LPKSAUB3O5ABSBFAJF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5OFZP4D5LPKSAUB3O5ABSBFAJF","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":"c1efa5c118a229949e4cf12f3c4b0bfe60ffa91fc60db429f3c2fe647ad86234","cross_cats_sorted":["gr-qc","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-09-18T10:44:23Z","title_canon_sha256":"27d92e8d58f90f830386292f91cebee9404993f3d5eeed78c7ee1767da0d6954"},"schema_version":"1.0","source":{"id":"2409.11866","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.11866","created_at":"2026-07-05T10:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"2409.11866v2","created_at":"2026-07-05T10:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.11866","created_at":"2026-07-05T10:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"5OFZP4D5LPKS","created_at":"2026-07-05T10:28:21Z"},{"alias_kind":"pith_short_16","alias_value":"5OFZP4D5LPKSAUB3","created_at":"2026-07-05T10:28:21Z"},{"alias_kind":"pith_short_8","alias_value":"5OFZP4D5","created_at":"2026-07-05T10:28:21Z"}],"graph_snapshots":[{"event_id":"sha256:28e72889e13b40d76d5ef4ebfe61d7a785089455957142516b819daa37eb167d","target":"graph","created_at":"2026-07-05T10:28:21Z","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/2409.11866/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a stochastic interpretation of spacetime non-commutativity starting from the path integral formulation of quantum mechanical commutation relations. We discuss how the (non-)commutativity of spacetime is inherently related to the continuity or discontinuity of paths in the path integral formulation. Utilizing Wiener processes, we demonstrate that continuous paths lead to commutative spacetime, whereas discontinuous paths correspond to non-commutative spacetime structures. As an example we introduce discontinuous paths from which the $\\kappa$-Minkowski spacetime commutators can be obt","authors_text":"Folkert Kuipers, Michele Arzano","cross_cats":["gr-qc","math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-09-18T10:44:23Z","title":"A Stochastic Origin of Spacetime Non-Commutativity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.11866","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":"sha256:69a0a0af6d9c2790158c2c221e98bb86168d8a7a621d1d30951891f37738291b","target":"record","created_at":"2026-07-05T10:28:21Z","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":"c1efa5c118a229949e4cf12f3c4b0bfe60ffa91fc60db429f3c2fe647ad86234","cross_cats_sorted":["gr-qc","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-09-18T10:44:23Z","title_canon_sha256":"27d92e8d58f90f830386292f91cebee9404993f3d5eeed78c7ee1767da0d6954"},"schema_version":"1.0","source":{"id":"2409.11866","kind":"arxiv","version":2}},"canonical_sha256":"eb8b97f07d5bd520503b77401904a0496e2c3916799ab60f8dfa55a8d8430382","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb8b97f07d5bd520503b77401904a0496e2c3916799ab60f8dfa55a8d8430382","first_computed_at":"2026-07-05T10:28:21.882585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:28:21.882585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ef8fZoUz/0EKqRwesGW+vTocE9PXkvvQ0CIuRoMDEW5xn2nNg8epGG2mcqha+SibIN5riWj8XHZ0J1OFL43XCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:28:21.883021Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.11866","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69a0a0af6d9c2790158c2c221e98bb86168d8a7a621d1d30951891f37738291b","sha256:28e72889e13b40d76d5ef4ebfe61d7a785089455957142516b819daa37eb167d"],"state_sha256":"e27c50a2bf7934d15ed449edaff702b93e379330493a17d9a72db9a83d1e8b7c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wNn1b0eBxlKDhHak/kQIFzIsJ29wbyJ2d/++c6ld7hvFnNwGGeHfAq4nQVwH82a4dNTIvkuWoUSdoDre283YDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T21:24:09.749392Z","bundle_sha256":"a617971e53b2aaf5152d721bcf849748d169faea83bdbb40a47cb63a05676afc"}}