{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YXQR4AVKT5BEZJ4IHC53RQ2XGJ","short_pith_number":"pith:YXQR4AVK","canonical_record":{"source":{"id":"1504.03265","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-04-13T17:26:26Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"49084107b80c97f00b5f7601c05a266f8337078522e6287d387287da0d0d3c18","abstract_canon_sha256":"72cfba365005f8235fb7df04613cefe999c9de7a36fce30a09bbf181e6b0243c"},"schema_version":"1.0"},"canonical_sha256":"c5e11e02aa9f424ca78838bbb8c3573245d50734a5260de5e38d20fad10e54e2","source":{"kind":"arxiv","id":"1504.03265","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03265","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03265v2","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03265","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"YXQR4AVKT5BE","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YXQR4AVKT5BEZJ4I","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YXQR4AVK","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YXQR4AVKT5BEZJ4IHC53RQ2XGJ","target":"record","payload":{"canonical_record":{"source":{"id":"1504.03265","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-04-13T17:26:26Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"49084107b80c97f00b5f7601c05a266f8337078522e6287d387287da0d0d3c18","abstract_canon_sha256":"72cfba365005f8235fb7df04613cefe999c9de7a36fce30a09bbf181e6b0243c"},"schema_version":"1.0"},"canonical_sha256":"c5e11e02aa9f424ca78838bbb8c3573245d50734a5260de5e38d20fad10e54e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:58.566338Z","signature_b64":"5riIPVqagFUn8w4EFlOAStnof7z2gqnAWAEPv7tHR5IGC0s8HmV1Zf8AzfIkGpI2S+m3Ufrwz+aBde9yyT1VDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5e11e02aa9f424ca78838bbb8c3573245d50734a5260de5e38d20fad10e54e2","last_reissued_at":"2026-05-18T01:12:58.565983Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:58.565983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.03265","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":"2026-05-18T01:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f9gMiE9qTYUtXDxKEifGqo6F2aNam1en4LRBEE02plWpHXGYvkaTyvKqTzWhIT+DlSVReWCSJqSqj0O+AgrtDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T11:26:55.173909Z"},"content_sha256":"f78f32c5c2fb57a174b494b777feaa9b88dea14ef83151a913a5e1d2e63d516e","schema_version":"1.0","event_id":"sha256:f78f32c5c2fb57a174b494b777feaa9b88dea14ef83151a913a5e1d2e63d516e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YXQR4AVKT5BEZJ4IHC53RQ2XGJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spacetime causal structure and dimension from horismotic relation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Ovidiu Cristinel Stoica","submitted_at":"2015-04-13T17:26:26Z","abstract_excerpt":"A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated events (the horismos relation), we can construct in a natural way the entire causal structure: causal and chronological relations, causal curves, and a topology. By imposing a simple additional condition, the structure gains a definite number of dimensions. This construction works both with continuous and discrete spacetimes. The dimensionality is obtained "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03265","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":""},"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":"2026-05-18T01:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BGC7UIG+m3sd9Oh3uBi/pwuUvgUYOji4SflViD7DAXGFmJlTd1ylPjRcVdzqZor8kv6KyXykeE7+hCjxn2aZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T11:26:55.174581Z"},"content_sha256":"902b80c744a16d3876d509d19784c6b9fc9a0a8ffade16f1ae9dd62615fb82a0","schema_version":"1.0","event_id":"sha256:902b80c744a16d3876d509d19784c6b9fc9a0a8ffade16f1ae9dd62615fb82a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YXQR4AVKT5BEZJ4IHC53RQ2XGJ/bundle.json","state_url":"https://pith.science/pith/YXQR4AVKT5BEZJ4IHC53RQ2XGJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YXQR4AVKT5BEZJ4IHC53RQ2XGJ/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":"2026-06-06T11:26:55Z","links":{"resolver":"https://pith.science/pith/YXQR4AVKT5BEZJ4IHC53RQ2XGJ","bundle":"https://pith.science/pith/YXQR4AVKT5BEZJ4IHC53RQ2XGJ/bundle.json","state":"https://pith.science/pith/YXQR4AVKT5BEZJ4IHC53RQ2XGJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YXQR4AVKT5BEZJ4IHC53RQ2XGJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YXQR4AVKT5BEZJ4IHC53RQ2XGJ","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":"72cfba365005f8235fb7df04613cefe999c9de7a36fce30a09bbf181e6b0243c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-04-13T17:26:26Z","title_canon_sha256":"49084107b80c97f00b5f7601c05a266f8337078522e6287d387287da0d0d3c18"},"schema_version":"1.0","source":{"id":"1504.03265","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03265","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03265v2","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03265","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"YXQR4AVKT5BE","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YXQR4AVKT5BEZJ4I","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YXQR4AVK","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:902b80c744a16d3876d509d19784c6b9fc9a0a8ffade16f1ae9dd62615fb82a0","target":"graph","created_at":"2026-05-18T01:12:58Z","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":"A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated events (the horismos relation), we can construct in a natural way the entire causal structure: causal and chronological relations, causal curves, and a topology. By imposing a simple additional condition, the structure gains a definite number of dimensions. This construction works both with continuous and discrete spacetimes. The dimensionality is obtained ","authors_text":"Ovidiu Cristinel Stoica","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-04-13T17:26:26Z","title":"Spacetime causal structure and dimension from horismotic relation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03265","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:f78f32c5c2fb57a174b494b777feaa9b88dea14ef83151a913a5e1d2e63d516e","target":"record","created_at":"2026-05-18T01:12:58Z","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":"72cfba365005f8235fb7df04613cefe999c9de7a36fce30a09bbf181e6b0243c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-04-13T17:26:26Z","title_canon_sha256":"49084107b80c97f00b5f7601c05a266f8337078522e6287d387287da0d0d3c18"},"schema_version":"1.0","source":{"id":"1504.03265","kind":"arxiv","version":2}},"canonical_sha256":"c5e11e02aa9f424ca78838bbb8c3573245d50734a5260de5e38d20fad10e54e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5e11e02aa9f424ca78838bbb8c3573245d50734a5260de5e38d20fad10e54e2","first_computed_at":"2026-05-18T01:12:58.565983Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:58.565983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5riIPVqagFUn8w4EFlOAStnof7z2gqnAWAEPv7tHR5IGC0s8HmV1Zf8AzfIkGpI2S+m3Ufrwz+aBde9yyT1VDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:58.566338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.03265","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f78f32c5c2fb57a174b494b777feaa9b88dea14ef83151a913a5e1d2e63d516e","sha256:902b80c744a16d3876d509d19784c6b9fc9a0a8ffade16f1ae9dd62615fb82a0"],"state_sha256":"a81b85828d1c671ffc9f75021053d20bc7272c0aa18bb425fc876c136878d83d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m10gsbP6uglQMcXDlNB8Cx0A5ymI8cPgNl387dnEGIEjMaY859ivfAx+JHH7fSJ4ymjm3/6k0wmXGJBPcxMVCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T11:26:55.178803Z","bundle_sha256":"ccb7329a388046630b31fc483bd351fb5f0a7b3a9674930b5aa4a40a1e264989"}}