{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:Y76JL27F7KORCASC3S54USOZWY","short_pith_number":"pith:Y76JL27F","canonical_record":{"source":{"id":"math/0109057","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2001-09-09T17:21:52Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"aa3a6d09c99112f829eb5daefa85e9460c24dc032bb1f4a27b14784eda1bc878","abstract_canon_sha256":"bf269fd241b5ccbc0b0671ce5ee1ea2fece0fa9caf2c35a82a593930ae7f6b7d"},"schema_version":"1.0"},"canonical_sha256":"c7fc95ebe5fa9d110242dcbbca49d9b63e8db5e77fd39cb65f67765376ce7618","source":{"kind":"arxiv","id":"math/0109057","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0109057","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"arxiv_version","alias_value":"math/0109057v3","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0109057","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"pith_short_12","alias_value":"Y76JL27F7KOR","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"Y76JL27F7KORCASC","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"Y76JL27F","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:Y76JL27F7KORCASC3S54USOZWY","target":"record","payload":{"canonical_record":{"source":{"id":"math/0109057","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2001-09-09T17:21:52Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"aa3a6d09c99112f829eb5daefa85e9460c24dc032bb1f4a27b14784eda1bc878","abstract_canon_sha256":"bf269fd241b5ccbc0b0671ce5ee1ea2fece0fa9caf2c35a82a593930ae7f6b7d"},"schema_version":"1.0"},"canonical_sha256":"c7fc95ebe5fa9d110242dcbbca49d9b63e8db5e77fd39cb65f67765376ce7618","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:09.425805Z","signature_b64":"qcgb15KTPk//wsFMu2cpojR5R5U1KJiqqVYIb/t0OJxhpgwqjkBU+dlSmxLGjGwMfUbGgPGeT86lbwgTV72nCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7fc95ebe5fa9d110242dcbbca49d9b63e8db5e77fd39cb65f67765376ce7618","last_reissued_at":"2026-05-18T01:25:09.425221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:09.425221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0109057","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":"2026-05-18T01:25:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y3N4NdQHBydl/BHwO7xn/QTfg13mp7ZUkN8PH6wdTj4XGBW0LXUtWH57HWg/vg+18rcycC5tE5uOur0PGerQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:16:20.999703Z"},"content_sha256":"565f2015db8faf097ac71ea22fba9a0ff9945603e8c97ee7f053ba87ab009cff","schema_version":"1.0","event_id":"sha256:565f2015db8faf097ac71ea22fba9a0ff9945603e8c97ee7f053ba87ab009cff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:Y76JL27F7KORCASC3S54USOZWY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multicomplexes, bounded cohomology and additivity of simplicial volume","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Thilo Kuessner","submitted_at":"2001-09-09T17:21:52Z","abstract_excerpt":"We discuss some additivity properties of the simplicial volume for manifolds with boundary: we give proofs of additivity for glueing amenable boundary components and of superadditivity for glueing amenable submanifolds of the boundary, and we discuss doubling of 3-manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0109057","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":"2026-05-18T01:25:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1bHGNnWJ1BDn07pjTQLiXcVEyQoJ3wXdUnhFZSV9YOkMGNNgb59VFt+ddOxBZx0CPN3T6XzPRnf3ouWtCE8RDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:16:21.000045Z"},"content_sha256":"1e05da9dad72b6186c37f2b2ac96e78b8c86bb00bd4d7a0e36cda9fb2ed449ab","schema_version":"1.0","event_id":"sha256:1e05da9dad72b6186c37f2b2ac96e78b8c86bb00bd4d7a0e36cda9fb2ed449ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y76JL27F7KORCASC3S54USOZWY/bundle.json","state_url":"https://pith.science/pith/Y76JL27F7KORCASC3S54USOZWY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y76JL27F7KORCASC3S54USOZWY/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":"2026-06-23T06:16:21Z","links":{"resolver":"https://pith.science/pith/Y76JL27F7KORCASC3S54USOZWY","bundle":"https://pith.science/pith/Y76JL27F7KORCASC3S54USOZWY/bundle.json","state":"https://pith.science/pith/Y76JL27F7KORCASC3S54USOZWY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y76JL27F7KORCASC3S54USOZWY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:Y76JL27F7KORCASC3S54USOZWY","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":"bf269fd241b5ccbc0b0671ce5ee1ea2fece0fa9caf2c35a82a593930ae7f6b7d","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2001-09-09T17:21:52Z","title_canon_sha256":"aa3a6d09c99112f829eb5daefa85e9460c24dc032bb1f4a27b14784eda1bc878"},"schema_version":"1.0","source":{"id":"math/0109057","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0109057","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"arxiv_version","alias_value":"math/0109057v3","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0109057","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"pith_short_12","alias_value":"Y76JL27F7KOR","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"Y76JL27F7KORCASC","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"Y76JL27F","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:1e05da9dad72b6186c37f2b2ac96e78b8c86bb00bd4d7a0e36cda9fb2ed449ab","target":"graph","created_at":"2026-05-18T01:25:09Z","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 discuss some additivity properties of the simplicial volume for manifolds with boundary: we give proofs of additivity for glueing amenable boundary components and of superadditivity for glueing amenable submanifolds of the boundary, and we discuss doubling of 3-manifolds.","authors_text":"Thilo Kuessner","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2001-09-09T17:21:52Z","title":"Multicomplexes, bounded cohomology and additivity of simplicial volume"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0109057","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":"sha256:565f2015db8faf097ac71ea22fba9a0ff9945603e8c97ee7f053ba87ab009cff","target":"record","created_at":"2026-05-18T01:25:09Z","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":"bf269fd241b5ccbc0b0671ce5ee1ea2fece0fa9caf2c35a82a593930ae7f6b7d","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2001-09-09T17:21:52Z","title_canon_sha256":"aa3a6d09c99112f829eb5daefa85e9460c24dc032bb1f4a27b14784eda1bc878"},"schema_version":"1.0","source":{"id":"math/0109057","kind":"arxiv","version":3}},"canonical_sha256":"c7fc95ebe5fa9d110242dcbbca49d9b63e8db5e77fd39cb65f67765376ce7618","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7fc95ebe5fa9d110242dcbbca49d9b63e8db5e77fd39cb65f67765376ce7618","first_computed_at":"2026-05-18T01:25:09.425221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:09.425221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qcgb15KTPk//wsFMu2cpojR5R5U1KJiqqVYIb/t0OJxhpgwqjkBU+dlSmxLGjGwMfUbGgPGeT86lbwgTV72nCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:09.425805Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0109057","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:565f2015db8faf097ac71ea22fba9a0ff9945603e8c97ee7f053ba87ab009cff","sha256:1e05da9dad72b6186c37f2b2ac96e78b8c86bb00bd4d7a0e36cda9fb2ed449ab"],"state_sha256":"843cdeac7ab6018cb48d37accd3a48642ce6c4c736731f84fac57e47814273e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"csc5oCwv5Obi/c0P0T6PHN521F/lnZhKMk2nl6c0EK6qr0Zr5jIaG/wCW1zeI9s9ObSHf6YMMdGaO30sqY9cAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:16:21.001991Z","bundle_sha256":"8257befda147f51576b97454849dbe89f0d1e57923c56fb69ae35101bfb6046c"}}