{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TLCIB5VUNPCWQV2GYO6FDUNFZW","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":"d190abebce9ca8d0e848943541d9c05467da6be82cfa26f8e9c6f6671fa3d919","cross_cats_sorted":["math.AT","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-02-14T17:25:03Z","title_canon_sha256":"84a1e8719d0929b663fb8ac7e4226b559c03f56ff0fb345bae329959149e4ac6"},"schema_version":"1.0","source":{"id":"1802.05223","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.05223","created_at":"2026-05-17T23:48:52Z"},{"alias_kind":"arxiv_version","alias_value":"1802.05223v2","created_at":"2026-05-17T23:48:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.05223","created_at":"2026-05-17T23:48:52Z"},{"alias_kind":"pith_short_12","alias_value":"TLCIB5VUNPCW","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TLCIB5VUNPCWQV2G","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TLCIB5VU","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:b60fa70bd825fbd35403e6dd9373c8f972bb51e63a18018eb882a60a1b36cf5d","target":"graph","created_at":"2026-05-17T23:48:52Z","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 define the ideal simplicial volume for compact manifolds with boundary. Roughly speaking, the ideal simplicial volume of a manifold $M$ measures the minimal size of possibly ideal triangulations of $M$ \"with real coefficients\", thus providing a variation of the ordinary simplicial volume defined by Gromov in 1982, the main difference being that ideal simplices are now allowed to appear in representatives of the fundamental class.\n  We show that the ideal simplicial volume is bounded above by the ordinary simplicial volume, and that it vanishes if and only if the ordinary simplicial volume d","authors_text":"Marco Moraschini, Roberto Frigerio","cross_cats":["math.AT","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-02-14T17:25:03Z","title":"Ideal simplicial volume of manifolds with boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05223","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:b76110271841fc55a66cc9762c4be055f9d6c45d73c3264954b6d739b4cdeb21","target":"record","created_at":"2026-05-17T23:48:52Z","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":"d190abebce9ca8d0e848943541d9c05467da6be82cfa26f8e9c6f6671fa3d919","cross_cats_sorted":["math.AT","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-02-14T17:25:03Z","title_canon_sha256":"84a1e8719d0929b663fb8ac7e4226b559c03f56ff0fb345bae329959149e4ac6"},"schema_version":"1.0","source":{"id":"1802.05223","kind":"arxiv","version":2}},"canonical_sha256":"9ac480f6b46bc5685746c3bc51d1a5cdad0ad878f83fc35c28f9e8acebddb63c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ac480f6b46bc5685746c3bc51d1a5cdad0ad878f83fc35c28f9e8acebddb63c","first_computed_at":"2026-05-17T23:48:52.985636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:52.985636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DyNXt/PUsNzyTopeJYhJ12lt53bqvWfxZRHVHRE3lblGOYi+onWRbJ2IKvPpaL+cLGqVgvAEPFBc6lB8y6/ADA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:52.986129Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.05223","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b76110271841fc55a66cc9762c4be055f9d6c45d73c3264954b6d739b4cdeb21","sha256:b60fa70bd825fbd35403e6dd9373c8f972bb51e63a18018eb882a60a1b36cf5d"],"state_sha256":"efa085e502443cbbf89bcc44ebdebbc7ea4d97779171962fdc21e4a8d0f513c6"}