{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PCA6DAYG4LKU3CULURG2E6PUEF","short_pith_number":"pith:PCA6DAYG","canonical_record":{"source":{"id":"1205.2117","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-05-09T22:42:02Z","cross_cats_sorted":[],"title_canon_sha256":"e5a88439c1794eed0f4fcfe984a268b58d9488c19f650a3bbdba1824a6fc0399","abstract_canon_sha256":"59e7e332726b71ea0481ca4cb37fad802ba4e8b710d96c9caf9ae867bc09b6d8"},"schema_version":"1.0"},"canonical_sha256":"7881e18306e2d54d8a8ba44da279f4216330d798a60814adfca46ad916ce4a59","source":{"kind":"arxiv","id":"1205.2117","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2117","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2117v3","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2117","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"pith_short_12","alias_value":"PCA6DAYG4LKU","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PCA6DAYG4LKU3CUL","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PCA6DAYG","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PCA6DAYG4LKU3CULURG2E6PUEF","target":"record","payload":{"canonical_record":{"source":{"id":"1205.2117","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-05-09T22:42:02Z","cross_cats_sorted":[],"title_canon_sha256":"e5a88439c1794eed0f4fcfe984a268b58d9488c19f650a3bbdba1824a6fc0399","abstract_canon_sha256":"59e7e332726b71ea0481ca4cb37fad802ba4e8b710d96c9caf9ae867bc09b6d8"},"schema_version":"1.0"},"canonical_sha256":"7881e18306e2d54d8a8ba44da279f4216330d798a60814adfca46ad916ce4a59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:15.967611Z","signature_b64":"XfeE5hBSPW2bRbt8w87KjcrqrpZBDhvD2XR81630LiFgHf/DDBV5cESPDzPzhA33ng2HIdqMifEudSi1jJZjDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7881e18306e2d54d8a8ba44da279f4216330d798a60814adfca46ad916ce4a59","last_reissued_at":"2026-05-18T01:36:15.966874Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:15.966874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.2117","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4pEqxRH1LPGqkumXb9JrDBSAEr7WStBQJvrwJE/pgzUTHBXZw3b2ueby2+/73RJsDuJsMCe/1AA3gnD0muMaCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:27:38.562769Z"},"content_sha256":"de80adfe5fa4bda857cdf6b0be27e748001d9a634b3092f27ee296a8c708e719","schema_version":"1.0","event_id":"sha256:de80adfe5fa4bda857cdf6b0be27e748001d9a634b3092f27ee296a8c708e719"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PCA6DAYG4LKU3CULURG2E6PUEF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unique Parallel Decomposition in Branching and Weak Bisimulation Semantics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Bas Luttik","submitted_at":"2012-05-09T22:42:02Z","abstract_excerpt":"We consider the property of unique parallel decomposition modulo branching and weak bisimilarity. First, we show that infinite behaviours may fail to have parallel decompositions at all. Then, we prove that totally normed behaviours always have parallel decompositions, but that these are not necessarily unique. Finally, we establish that weakly bounded behaviours have unique parallel decompositions. We derive the latter result from a general theorem about unique decompositions in partial commutative monoids."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2117","kind":"arxiv","version":3},"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":"2026-05-18T01:36:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T3Be/tPWyXwvgww4G+hW26ru+mqSHh8FvMTA8Cc+gsXnZ1DvxlCRjBbyKROFeHXidvjNw/rB1p4WzM3tkBKQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:27:38.563113Z"},"content_sha256":"9e705afeb7f96e1d87ed162e08db6ad77c347bd0b93f49b726139ca0f0ab145c","schema_version":"1.0","event_id":"sha256:9e705afeb7f96e1d87ed162e08db6ad77c347bd0b93f49b726139ca0f0ab145c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PCA6DAYG4LKU3CULURG2E6PUEF/bundle.json","state_url":"https://pith.science/pith/PCA6DAYG4LKU3CULURG2E6PUEF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PCA6DAYG4LKU3CULURG2E6PUEF/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":"2026-05-28T03:27:38Z","links":{"resolver":"https://pith.science/pith/PCA6DAYG4LKU3CULURG2E6PUEF","bundle":"https://pith.science/pith/PCA6DAYG4LKU3CULURG2E6PUEF/bundle.json","state":"https://pith.science/pith/PCA6DAYG4LKU3CULURG2E6PUEF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PCA6DAYG4LKU3CULURG2E6PUEF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PCA6DAYG4LKU3CULURG2E6PUEF","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":"59e7e332726b71ea0481ca4cb37fad802ba4e8b710d96c9caf9ae867bc09b6d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-05-09T22:42:02Z","title_canon_sha256":"e5a88439c1794eed0f4fcfe984a268b58d9488c19f650a3bbdba1824a6fc0399"},"schema_version":"1.0","source":{"id":"1205.2117","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2117","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2117v3","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2117","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"pith_short_12","alias_value":"PCA6DAYG4LKU","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PCA6DAYG4LKU3CUL","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PCA6DAYG","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:9e705afeb7f96e1d87ed162e08db6ad77c347bd0b93f49b726139ca0f0ab145c","target":"graph","created_at":"2026-05-18T01:36:15Z","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":"We consider the property of unique parallel decomposition modulo branching and weak bisimilarity. First, we show that infinite behaviours may fail to have parallel decompositions at all. Then, we prove that totally normed behaviours always have parallel decompositions, but that these are not necessarily unique. Finally, we establish that weakly bounded behaviours have unique parallel decompositions. We derive the latter result from a general theorem about unique decompositions in partial commutative monoids.","authors_text":"Bas Luttik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-05-09T22:42:02Z","title":"Unique Parallel Decomposition in Branching and Weak Bisimulation Semantics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2117","kind":"arxiv","version":3},"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:de80adfe5fa4bda857cdf6b0be27e748001d9a634b3092f27ee296a8c708e719","target":"record","created_at":"2026-05-18T01:36:15Z","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":"59e7e332726b71ea0481ca4cb37fad802ba4e8b710d96c9caf9ae867bc09b6d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-05-09T22:42:02Z","title_canon_sha256":"e5a88439c1794eed0f4fcfe984a268b58d9488c19f650a3bbdba1824a6fc0399"},"schema_version":"1.0","source":{"id":"1205.2117","kind":"arxiv","version":3}},"canonical_sha256":"7881e18306e2d54d8a8ba44da279f4216330d798a60814adfca46ad916ce4a59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7881e18306e2d54d8a8ba44da279f4216330d798a60814adfca46ad916ce4a59","first_computed_at":"2026-05-18T01:36:15.966874Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:15.966874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XfeE5hBSPW2bRbt8w87KjcrqrpZBDhvD2XR81630LiFgHf/DDBV5cESPDzPzhA33ng2HIdqMifEudSi1jJZjDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:15.967611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2117","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de80adfe5fa4bda857cdf6b0be27e748001d9a634b3092f27ee296a8c708e719","sha256:9e705afeb7f96e1d87ed162e08db6ad77c347bd0b93f49b726139ca0f0ab145c"],"state_sha256":"6904e7a246cdd36788caf8f4447c0b70121befe3fc3c78e807c766d0e85fbf41"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FtMjrp5OgGrCDc79Q3AfLszrlidDIXWT2drSai9uGw+vSEy9HTegpFtxfgRurZWE7tgXkUcoyTY4ci1Q7J4gDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:27:38.565120Z","bundle_sha256":"c81d9c277e15c334765cdc2b91c06643e7aa14666836dd81c5a7661c056c1c7a"}}