{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MISON75UFUYUABLXCT72M6HABN","short_pith_number":"pith:MISON75U","canonical_record":{"source":{"id":"1506.02270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-06-07T14:34:53Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"164b148ccb2ae6b869c5168a64512d867bd662547c0de67cce88f2378450b5c0","abstract_canon_sha256":"a171b0d87e564815d7102fce44a776f3b0dddc4d0e44b4223126d50149f34d2e"},"schema_version":"1.0"},"canonical_sha256":"6224e6ffb42d3140057714ffa678e00b41a0c036d6d073b23dd5632f69b7bab3","source":{"kind":"arxiv","id":"1506.02270","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02270","created_at":"2026-05-18T01:55:51Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02270v1","created_at":"2026-05-18T01:55:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02270","created_at":"2026-05-18T01:55:51Z"},{"alias_kind":"pith_short_12","alias_value":"MISON75UFUYU","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MISON75UFUYUABLX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MISON75U","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MISON75UFUYUABLXCT72M6HABN","target":"record","payload":{"canonical_record":{"source":{"id":"1506.02270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-06-07T14:34:53Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"164b148ccb2ae6b869c5168a64512d867bd662547c0de67cce88f2378450b5c0","abstract_canon_sha256":"a171b0d87e564815d7102fce44a776f3b0dddc4d0e44b4223126d50149f34d2e"},"schema_version":"1.0"},"canonical_sha256":"6224e6ffb42d3140057714ffa678e00b41a0c036d6d073b23dd5632f69b7bab3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:51.675148Z","signature_b64":"mF6fAiG10e9lMmA11UPu+3EpA7UXxLD8Vc2XdZ+R2N+GOq+WyAc1vQQ26t8CTrwk9P36whLow2GGYJtMOJkuBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6224e6ffb42d3140057714ffa678e00b41a0c036d6d073b23dd5632f69b7bab3","last_reissued_at":"2026-05-18T01:55:51.674548Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:51.674548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.02270","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":"2026-05-18T01:55:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3pAJ1/33yQJBDwQotIOji2sASUOCBx7HpYFk0LM9H5A+9VQBbS7G7R8z5cQC3XB9jx5YooqN3sBm3cLEBgG8AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T09:41:16.892500Z"},"content_sha256":"e6acb00375b3173f186a622da7bac3fb47d80e4030989fdb9255327580bfc79d","schema_version":"1.0","event_id":"sha256:e6acb00375b3173f186a622da7bac3fb47d80e4030989fdb9255327580bfc79d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MISON75UFUYUABLXCT72M6HABN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological abstraction of higher-dimensional automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"cs.FL","authors_text":"Thomas Kahl","submitted_at":"2015-06-07T14:34:53Z","abstract_excerpt":"Higher-dimensional automata constitute a very expressive model for concurrent systems. In this paper, we discuss \"topological abstraction\" of higher-dimensional automata, i.e., the replacement of HDAs by smaller ones that can be considered equivalent from both a computer scientific and a topological point of view. By definition, topological abstraction preserves the homotopy type, the trace category, and the homology graph of an HDA. We establish conditions under which cube collapses yield topological abstractions of HDAs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02270","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":""},"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":"2026-05-18T01:55:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6FXEMiMXR+F6WBTpDzjj8YEQWPcOPyXzbotOTUWGXBZ+UNyAqbLpGTVm46Z+DBBnng58GVhZDSyr8OUErAKxBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T09:41:16.892847Z"},"content_sha256":"6b96f59d21921cdc211faa2d9739b8975b2a918a98c40beb4264fdd2d4e5d027","schema_version":"1.0","event_id":"sha256:6b96f59d21921cdc211faa2d9739b8975b2a918a98c40beb4264fdd2d4e5d027"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MISON75UFUYUABLXCT72M6HABN/bundle.json","state_url":"https://pith.science/pith/MISON75UFUYUABLXCT72M6HABN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MISON75UFUYUABLXCT72M6HABN/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":"2026-06-24T09:41:16Z","links":{"resolver":"https://pith.science/pith/MISON75UFUYUABLXCT72M6HABN","bundle":"https://pith.science/pith/MISON75UFUYUABLXCT72M6HABN/bundle.json","state":"https://pith.science/pith/MISON75UFUYUABLXCT72M6HABN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MISON75UFUYUABLXCT72M6HABN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MISON75UFUYUABLXCT72M6HABN","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":"a171b0d87e564815d7102fce44a776f3b0dddc4d0e44b4223126d50149f34d2e","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-06-07T14:34:53Z","title_canon_sha256":"164b148ccb2ae6b869c5168a64512d867bd662547c0de67cce88f2378450b5c0"},"schema_version":"1.0","source":{"id":"1506.02270","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02270","created_at":"2026-05-18T01:55:51Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02270v1","created_at":"2026-05-18T01:55:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02270","created_at":"2026-05-18T01:55:51Z"},{"alias_kind":"pith_short_12","alias_value":"MISON75UFUYU","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MISON75UFUYUABLX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MISON75U","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:6b96f59d21921cdc211faa2d9739b8975b2a918a98c40beb4264fdd2d4e5d027","target":"graph","created_at":"2026-05-18T01:55:51Z","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":"Higher-dimensional automata constitute a very expressive model for concurrent systems. In this paper, we discuss \"topological abstraction\" of higher-dimensional automata, i.e., the replacement of HDAs by smaller ones that can be considered equivalent from both a computer scientific and a topological point of view. By definition, topological abstraction preserves the homotopy type, the trace category, and the homology graph of an HDA. We establish conditions under which cube collapses yield topological abstractions of HDAs.","authors_text":"Thomas Kahl","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-06-07T14:34:53Z","title":"Topological abstraction of higher-dimensional automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02270","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:e6acb00375b3173f186a622da7bac3fb47d80e4030989fdb9255327580bfc79d","target":"record","created_at":"2026-05-18T01:55:51Z","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":"a171b0d87e564815d7102fce44a776f3b0dddc4d0e44b4223126d50149f34d2e","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-06-07T14:34:53Z","title_canon_sha256":"164b148ccb2ae6b869c5168a64512d867bd662547c0de67cce88f2378450b5c0"},"schema_version":"1.0","source":{"id":"1506.02270","kind":"arxiv","version":1}},"canonical_sha256":"6224e6ffb42d3140057714ffa678e00b41a0c036d6d073b23dd5632f69b7bab3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6224e6ffb42d3140057714ffa678e00b41a0c036d6d073b23dd5632f69b7bab3","first_computed_at":"2026-05-18T01:55:51.674548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:51.674548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mF6fAiG10e9lMmA11UPu+3EpA7UXxLD8Vc2XdZ+R2N+GOq+WyAc1vQQ26t8CTrwk9P36whLow2GGYJtMOJkuBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:51.675148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02270","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6acb00375b3173f186a622da7bac3fb47d80e4030989fdb9255327580bfc79d","sha256:6b96f59d21921cdc211faa2d9739b8975b2a918a98c40beb4264fdd2d4e5d027"],"state_sha256":"1bbff4270e715b42eb9bf370432fdf302033738516eb0c489628d2c18e38c483"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r4SBJlRLS3utbhu9n6qYB/WtIKS4VlbSspQZ1DZMfVzwPcHREOXiREV9IbVvXzFxGozmEZNiyt/grBfqnoroDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T09:41:16.894814Z","bundle_sha256":"242eee8ae70caface67a866ff26a7ebe4450c9fdf8a5bc07bc452331d0d07bb5"}}