{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZS2ZLBBSFAY4DBDLKWMYENTMG4","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":"09d50815152fdce5dfd5b4cae0f4dba163b861cd5b2a155babf98ebff224d55e","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-12-14T06:24:19Z","title_canon_sha256":"a79442177d07c163f37add16aeeffd2b6c7a54154d33007b0c8edffe2ff668fb"},"schema_version":"1.0","source":{"id":"1712.05103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05103","created_at":"2026-05-18T00:28:01Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05103v1","created_at":"2026-05-18T00:28:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05103","created_at":"2026-05-18T00:28:01Z"},{"alias_kind":"pith_short_12","alias_value":"ZS2ZLBBSFAY4","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZS2ZLBBSFAY4DBDL","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZS2ZLBBS","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:538ec29889c9b7755ce6fd37abf03b1ec4fbea3cd63811f1baf90ad06d11b7bf","target":"graph","created_at":"2026-05-18T00:28:01Z","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":"This paper shows a mathematical formalization, algorithms and computation software of volume optimal cycles, which are useful to understand geometric features shown in a persistence diagram. Volume optimal cycles give us concrete and optimal homologous structures, such as rings or cavities, on a given data. The key idea is the optimality on $(q + 1)$-chain complex for a $q$th homology generator. This optimality formalization is suitable for persistent homology. We can solve the optimization problem using linear programming. For an alpha filtration on $\\mathbb{R}^n$, volume optimal cycles on an","authors_text":"Ippei Obayashi","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-12-14T06:24:19Z","title":"Volume Optimal Cycle: Tightest representative cycle of a generator on persistent homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05103","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":"sha256:2f4205ed5ff32aa422a37d933972df0c6e941d52e9aa754e5a7a84d0c5055370","target":"record","created_at":"2026-05-18T00:28:01Z","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":"09d50815152fdce5dfd5b4cae0f4dba163b861cd5b2a155babf98ebff224d55e","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-12-14T06:24:19Z","title_canon_sha256":"a79442177d07c163f37add16aeeffd2b6c7a54154d33007b0c8edffe2ff668fb"},"schema_version":"1.0","source":{"id":"1712.05103","kind":"arxiv","version":1}},"canonical_sha256":"ccb59584322831c1846b559982366c3714d73b1f0f8f9fcf1218f26ad4aead77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccb59584322831c1846b559982366c3714d73b1f0f8f9fcf1218f26ad4aead77","first_computed_at":"2026-05-18T00:28:01.024535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:01.024535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X4rnaGDiscdNyII9keG31jqsoxcrCKI/fOYSWKBV1q4JgCG26UGnuMOfgTNwat/Xfv5iXCgOWKqU7p7CmdtdCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:01.025271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.05103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f4205ed5ff32aa422a37d933972df0c6e941d52e9aa754e5a7a84d0c5055370","sha256:538ec29889c9b7755ce6fd37abf03b1ec4fbea3cd63811f1baf90ad06d11b7bf"],"state_sha256":"98ccae39af64de150714b4d973308432c275a34a2ae27034cf33758b88d4f58e"}