{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:BTLJI6NNGOEKLQBYVP2JMX3IUM","short_pith_number":"pith:BTLJI6NN","canonical_record":{"source":{"id":"math/9904039","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CT","submitted_at":"1999-04-09T11:57:29Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"6744633ff376cefefb954e0a9f64680f96efb0a2d6b7c8d1761c15272f336da8","abstract_canon_sha256":"0ed4585b9c4bcdf3425b40b704ddc99d720c07c496f1a0c11ef60152d7a5a805"},"schema_version":"1.0"},"canonical_sha256":"0cd69479ad3388a5c038abf4965f68a33eb1f4a2b0b9c2c579d8ea575ad9381a","source":{"kind":"arxiv","id":"math/9904039","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9904039","created_at":"2026-07-04T14:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"math/9904039v1","created_at":"2026-07-04T14:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9904039","created_at":"2026-07-04T14:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"BTLJI6NNGOEK","created_at":"2026-07-04T14:41:06Z"},{"alias_kind":"pith_short_16","alias_value":"BTLJI6NNGOEKLQBY","created_at":"2026-07-04T14:41:06Z"},{"alias_kind":"pith_short_8","alias_value":"BTLJI6NN","created_at":"2026-07-04T14:41:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:BTLJI6NNGOEKLQBYVP2JMX3IUM","target":"record","payload":{"canonical_record":{"source":{"id":"math/9904039","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CT","submitted_at":"1999-04-09T11:57:29Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"6744633ff376cefefb954e0a9f64680f96efb0a2d6b7c8d1761c15272f336da8","abstract_canon_sha256":"0ed4585b9c4bcdf3425b40b704ddc99d720c07c496f1a0c11ef60152d7a5a805"},"schema_version":"1.0"},"canonical_sha256":"0cd69479ad3388a5c038abf4965f68a33eb1f4a2b0b9c2c579d8ea575ad9381a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:41:06.864206Z","signature_b64":"xC/Gu1VjR+55cBzbtqLgUhpHE+9KkYE5gAr+osRAK5sp7Cf70b3zmU1VDcT4j7kQ638Re5xOrSb1eIfvZvvHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0cd69479ad3388a5c038abf4965f68a33eb1f4a2b0b9c2c579d8ea575ad9381a","last_reissued_at":"2026-07-04T14:41:06.863797Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:41:06.863797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9904039","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":"2026-07-04T14:41:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yPC9XF8S40LZM7bzVTmeNTVMY33TBBmyvz5tjlFTSPH9MNBpZQfM9pqc1KgPYr8z88oyIxOtEmdw2pmUPNTaBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T17:24:50.721270Z"},"content_sha256":"3f7215c1d5003ddec819499c09e25d858e626365848bd96f5922028827c7d6b0","schema_version":"1.0","event_id":"sha256:3f7215c1d5003ddec819499c09e25d858e626365848bd96f5922028827c7d6b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:BTLJI6NNGOEKLQBYVP2JMX3IUM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Joins for (Augmented) Simplicial Sets","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"P.J. Ehlers, T. Porter","submitted_at":"1999-04-09T11:57:29Z","abstract_excerpt":"We introduce a notion of join for (augmented) simplicial sets generalising the classical join of geometric simplicial complexes. The definition comes naturally from the ordinal sum on the base simplicial category $\\Delta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9904039","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/math/9904039/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":"2026-07-04T14:41:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Svc2MZHQ/gI+yDsNGMbYPj458Qf3iokGkcQG91g9im86B2mjKyo1X2QdlX26mGSEMYqmvYrN66cRZB84R5sqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T17:24:50.721995Z"},"content_sha256":"53963701b0f8e72cfc575cef6ee529bf0e5a4fd359ab9c156a72767ce28186b3","schema_version":"1.0","event_id":"sha256:53963701b0f8e72cfc575cef6ee529bf0e5a4fd359ab9c156a72767ce28186b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BTLJI6NNGOEKLQBYVP2JMX3IUM/bundle.json","state_url":"https://pith.science/pith/BTLJI6NNGOEKLQBYVP2JMX3IUM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BTLJI6NNGOEKLQBYVP2JMX3IUM/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":"2026-07-31T17:24:50Z","links":{"resolver":"https://pith.science/pith/BTLJI6NNGOEKLQBYVP2JMX3IUM","bundle":"https://pith.science/pith/BTLJI6NNGOEKLQBYVP2JMX3IUM/bundle.json","state":"https://pith.science/pith/BTLJI6NNGOEKLQBYVP2JMX3IUM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BTLJI6NNGOEKLQBYVP2JMX3IUM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:BTLJI6NNGOEKLQBYVP2JMX3IUM","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":"0ed4585b9c4bcdf3425b40b704ddc99d720c07c496f1a0c11ef60152d7a5a805","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.CT","submitted_at":"1999-04-09T11:57:29Z","title_canon_sha256":"6744633ff376cefefb954e0a9f64680f96efb0a2d6b7c8d1761c15272f336da8"},"schema_version":"1.0","source":{"id":"math/9904039","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9904039","created_at":"2026-07-04T14:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"math/9904039v1","created_at":"2026-07-04T14:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9904039","created_at":"2026-07-04T14:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"BTLJI6NNGOEK","created_at":"2026-07-04T14:41:06Z"},{"alias_kind":"pith_short_16","alias_value":"BTLJI6NNGOEKLQBY","created_at":"2026-07-04T14:41:06Z"},{"alias_kind":"pith_short_8","alias_value":"BTLJI6NN","created_at":"2026-07-04T14:41:06Z"}],"graph_snapshots":[{"event_id":"sha256:53963701b0f8e72cfc575cef6ee529bf0e5a4fd359ab9c156a72767ce28186b3","target":"graph","created_at":"2026-07-04T14:41:06Z","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/math/9904039/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a notion of join for (augmented) simplicial sets generalising the classical join of geometric simplicial complexes. The definition comes naturally from the ordinal sum on the base simplicial category $\\Delta$.","authors_text":"P.J. Ehlers, T. Porter","cross_cats":["math.AT"],"headline":"","license":"","primary_cat":"math.CT","submitted_at":"1999-04-09T11:57:29Z","title":"Joins for (Augmented) Simplicial Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9904039","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":"sha256:3f7215c1d5003ddec819499c09e25d858e626365848bd96f5922028827c7d6b0","target":"record","created_at":"2026-07-04T14:41:06Z","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":"0ed4585b9c4bcdf3425b40b704ddc99d720c07c496f1a0c11ef60152d7a5a805","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.CT","submitted_at":"1999-04-09T11:57:29Z","title_canon_sha256":"6744633ff376cefefb954e0a9f64680f96efb0a2d6b7c8d1761c15272f336da8"},"schema_version":"1.0","source":{"id":"math/9904039","kind":"arxiv","version":1}},"canonical_sha256":"0cd69479ad3388a5c038abf4965f68a33eb1f4a2b0b9c2c579d8ea575ad9381a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0cd69479ad3388a5c038abf4965f68a33eb1f4a2b0b9c2c579d8ea575ad9381a","first_computed_at":"2026-07-04T14:41:06.863797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:41:06.863797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xC/Gu1VjR+55cBzbtqLgUhpHE+9KkYE5gAr+osRAK5sp7Cf70b3zmU1VDcT4j7kQ638Re5xOrSb1eIfvZvvHBA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:41:06.864206Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9904039","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f7215c1d5003ddec819499c09e25d858e626365848bd96f5922028827c7d6b0","sha256:53963701b0f8e72cfc575cef6ee529bf0e5a4fd359ab9c156a72767ce28186b3"],"state_sha256":"1b7d339e40f5d251b7d6ed38316fed59cb159fa605f445b8a5a529a80e5e7eb6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CkFcTxrWEVMrnD9o0M3og5WoXuj7zrvYyzROkequFI1Uo6f8mbimKmBYUg1DrsIvUNj2+ZkfXLjRBsYGJAqhAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-31T17:24:50.730018Z","bundle_sha256":"8abc12179b75717e1d7636451f743d678f688b127f207d1db70cba8123977a28"}}