{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XYPXE4F52ACUGQUTEQFAD7UXEI","short_pith_number":"pith:XYPXE4F5","canonical_record":{"source":{"id":"1804.10894","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-04-29T09:21:28Z","cross_cats_sorted":[],"title_canon_sha256":"9e5fa73ddaaaf5db4cb07745a4e672f5c965de63ca3d904418d96e4762ead5dd","abstract_canon_sha256":"f2b7bccb124e3c7768e5c92e05e3c86ff5db7cf6acc0e56f5731445d1f4b02fa"},"schema_version":"1.0"},"canonical_sha256":"be1f7270bdd005434293240a01fe97223581382aaee7b49137c409e4cd3954b7","source":{"kind":"arxiv","id":"1804.10894","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10894","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10894v2","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10894","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"XYPXE4F52ACU","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"XYPXE4F52ACUGQUT","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"XYPXE4F5","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XYPXE4F52ACUGQUTEQFAD7UXEI","target":"record","payload":{"canonical_record":{"source":{"id":"1804.10894","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-04-29T09:21:28Z","cross_cats_sorted":[],"title_canon_sha256":"9e5fa73ddaaaf5db4cb07745a4e672f5c965de63ca3d904418d96e4762ead5dd","abstract_canon_sha256":"f2b7bccb124e3c7768e5c92e05e3c86ff5db7cf6acc0e56f5731445d1f4b02fa"},"schema_version":"1.0"},"canonical_sha256":"be1f7270bdd005434293240a01fe97223581382aaee7b49137c409e4cd3954b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:19.306834Z","signature_b64":"gLxOaYUc8UarN4U+6V1nSBijBSqvxj01OGHWqTFacnwv9igwTsnxd1Md9IoQ+fExDAcGRIX8Gt/UMLKQmcRiBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be1f7270bdd005434293240a01fe97223581382aaee7b49137c409e4cd3954b7","last_reissued_at":"2026-05-17T23:58:19.306448Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:19.306448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.10894","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":"2026-05-17T23:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cbFf+QWjV2dOKeRBHQXXEbmGpJk1r+n1JPlmLD1gOuPdg9VnU6lBQO60Tg5FzLV0NlJWqCgK+zbdDtM9JdgaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:13:09.157071Z"},"content_sha256":"a1f661cf816d98c035b35354084f7776d7b7d4920f80bedd76799569fe0cc60f","schema_version":"1.0","event_id":"sha256:a1f661cf816d98c035b35354084f7776d7b7d4920f80bedd76799569fe0cc60f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XYPXE4F52ACUGQUTEQFAD7UXEI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trees in Partial Higher Dimensional Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"J\\'er\\'emy Dubut","submitted_at":"2018-04-29T09:21:28Z","abstract_excerpt":"In this paper, we give a new definition of partial Higher Dimension Automata using lax functors. This definition is simpler and more natural from a categorical point of view, but also matches more clearly the intuition that pHDA are Higher Dimensional Automata with some missing faces. We then focus on trees. Originally, for example in transition systems, trees are defined as those systems that have a unique path property. To understand what kind of unique property is needed in pHDA, we start by looking at trees as colimits of paths. This definition tells us that trees are exactly the pHDA with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10894","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":"2026-05-17T23:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rKfm6TqevgBcGAc1fb3E4bjOzhFIMcyuz9d9g8JBx0UDUHpCNrMPQhj6nvYhaHHlszB1NDy7WP5SCyzRtyZ4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:13:09.157844Z"},"content_sha256":"90d91095f08ac49c9944f6dbd7e55c1e1526e03c062135e25ce7c257d3e4a162","schema_version":"1.0","event_id":"sha256:90d91095f08ac49c9944f6dbd7e55c1e1526e03c062135e25ce7c257d3e4a162"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XYPXE4F52ACUGQUTEQFAD7UXEI/bundle.json","state_url":"https://pith.science/pith/XYPXE4F52ACUGQUTEQFAD7UXEI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XYPXE4F52ACUGQUTEQFAD7UXEI/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":"2026-05-31T03:13:09Z","links":{"resolver":"https://pith.science/pith/XYPXE4F52ACUGQUTEQFAD7UXEI","bundle":"https://pith.science/pith/XYPXE4F52ACUGQUTEQFAD7UXEI/bundle.json","state":"https://pith.science/pith/XYPXE4F52ACUGQUTEQFAD7UXEI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XYPXE4F52ACUGQUTEQFAD7UXEI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XYPXE4F52ACUGQUTEQFAD7UXEI","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":"f2b7bccb124e3c7768e5c92e05e3c86ff5db7cf6acc0e56f5731445d1f4b02fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-04-29T09:21:28Z","title_canon_sha256":"9e5fa73ddaaaf5db4cb07745a4e672f5c965de63ca3d904418d96e4762ead5dd"},"schema_version":"1.0","source":{"id":"1804.10894","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10894","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10894v2","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10894","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"XYPXE4F52ACU","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"XYPXE4F52ACUGQUT","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"XYPXE4F5","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:90d91095f08ac49c9944f6dbd7e55c1e1526e03c062135e25ce7c257d3e4a162","target":"graph","created_at":"2026-05-17T23:58:19Z","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":"In this paper, we give a new definition of partial Higher Dimension Automata using lax functors. This definition is simpler and more natural from a categorical point of view, but also matches more clearly the intuition that pHDA are Higher Dimensional Automata with some missing faces. We then focus on trees. Originally, for example in transition systems, trees are defined as those systems that have a unique path property. To understand what kind of unique property is needed in pHDA, we start by looking at trees as colimits of paths. This definition tells us that trees are exactly the pHDA with","authors_text":"J\\'er\\'emy Dubut","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-04-29T09:21:28Z","title":"Trees in Partial Higher Dimensional Automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10894","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:a1f661cf816d98c035b35354084f7776d7b7d4920f80bedd76799569fe0cc60f","target":"record","created_at":"2026-05-17T23:58:19Z","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":"f2b7bccb124e3c7768e5c92e05e3c86ff5db7cf6acc0e56f5731445d1f4b02fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-04-29T09:21:28Z","title_canon_sha256":"9e5fa73ddaaaf5db4cb07745a4e672f5c965de63ca3d904418d96e4762ead5dd"},"schema_version":"1.0","source":{"id":"1804.10894","kind":"arxiv","version":2}},"canonical_sha256":"be1f7270bdd005434293240a01fe97223581382aaee7b49137c409e4cd3954b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be1f7270bdd005434293240a01fe97223581382aaee7b49137c409e4cd3954b7","first_computed_at":"2026-05-17T23:58:19.306448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:19.306448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gLxOaYUc8UarN4U+6V1nSBijBSqvxj01OGHWqTFacnwv9igwTsnxd1Md9IoQ+fExDAcGRIX8Gt/UMLKQmcRiBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:19.306834Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.10894","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1f661cf816d98c035b35354084f7776d7b7d4920f80bedd76799569fe0cc60f","sha256:90d91095f08ac49c9944f6dbd7e55c1e1526e03c062135e25ce7c257d3e4a162"],"state_sha256":"bee7d4ab83b8b148058f30ddfa0301b631af378915c87ce0e7e697fd0a21fec1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JWdEmvsvkKEfEPo79jrUPkp+34Lb0l4mwoup+6FvSjm66Bp1ZJj0YIF5/wNh3HZZ9r0BP+7XWv8i9O1sQvyiBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:13:09.160869Z","bundle_sha256":"61823f9ba67aa915746e801c51852698f6c6135a53c6e607c161b0ea7bbdc66d"}}