{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UUN4XIJZTWCD2FTUC7V6QFXZLX","short_pith_number":"pith:UUN4XIJZ","canonical_record":{"source":{"id":"1801.06759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-21T03:37:26Z","cross_cats_sorted":["cs.CG","math.CO"],"title_canon_sha256":"d0cbd99a2e567e7d3b408adc36d228eca11c3dada473c83bf7de1cfedbaabca3","abstract_canon_sha256":"66426f717fd45d5db64f5cb8eae68660c67a52a4930fc63d75704ee3d0086a9e"},"schema_version":"1.0"},"canonical_sha256":"a51bcba1399d843d167417ebe816f95dd669727123b27670b6148ff1a59c44f9","source":{"kind":"arxiv","id":"1801.06759","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.06759","created_at":"2026-05-18T00:24:59Z"},{"alias_kind":"arxiv_version","alias_value":"1801.06759v1","created_at":"2026-05-18T00:24:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.06759","created_at":"2026-05-18T00:24:59Z"},{"alias_kind":"pith_short_12","alias_value":"UUN4XIJZTWCD","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UUN4XIJZTWCD2FTU","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UUN4XIJZ","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UUN4XIJZTWCD2FTUC7V6QFXZLX","target":"record","payload":{"canonical_record":{"source":{"id":"1801.06759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-21T03:37:26Z","cross_cats_sorted":["cs.CG","math.CO"],"title_canon_sha256":"d0cbd99a2e567e7d3b408adc36d228eca11c3dada473c83bf7de1cfedbaabca3","abstract_canon_sha256":"66426f717fd45d5db64f5cb8eae68660c67a52a4930fc63d75704ee3d0086a9e"},"schema_version":"1.0"},"canonical_sha256":"a51bcba1399d843d167417ebe816f95dd669727123b27670b6148ff1a59c44f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:59.142485Z","signature_b64":"S526yAzQOY6a5H1O5cQHFKyTFY9C2giXYopiptxt4DEB5TZcc6nFeAbMYIhMX0yNOJee87FYmib0BXK9u0TqCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a51bcba1399d843d167417ebe816f95dd669727123b27670b6148ff1a59c44f9","last_reissued_at":"2026-05-18T00:24:59.142007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:59.142007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.06759","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":"2026-05-18T00:24:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h1Dtdaldg4OVyUes54lk8bWfAGjL2I7EQ0SuvymYfzbtGudvrAV/jWhU7O9RuByzzygjSW+FiAin3yfcpds2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:17:42.449963Z"},"content_sha256":"cb0415bd39e3f1a2d79a8f4dac2f132c265c8e342804d22435edae8cd047b667","schema_version":"1.0","event_id":"sha256:cb0415bd39e3f1a2d79a8f4dac2f132c265c8e342804d22435edae8cd047b667"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UUN4XIJZTWCD2FTUC7V6QFXZLX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient algorithms for computing a minimal homology basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.CO"],"primary_cat":"math.AT","authors_text":"Tamal K. Dey, Tianqi Li, Yusu Wang","submitted_at":"2018-01-21T03:37:26Z","abstract_excerpt":"Efficient computation of shortest cycles which form a homology basis under $\\mathbb{Z}_2$-additions in a given simplicial complex $\\mathcal{K}$ has been researched actively in recent years. When the complex $\\mathcal{K}$ is a weighted graph with $n$ vertices and $m$ edges, the problem of computing a shortest (homology) cycle basis is known to be solvable in $O(m^2n/\\log n+ n^2m)$-time. Several works \\cite{borradaile2017minimum, greedy} have addressed the case when the complex $\\mathcal{K}$ is a $2$-manifold. The complexity of these algorithms depends on the rank $g$ of the one-dimensional homo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06759","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":"2026-05-18T00:24:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tlwjErFOEX1gq9d0l3MDCvZ0IQM5fb5ysUSRQkNU8kupa4OHvXs9sppykaV5dM93goWh4DPBcobXh1eFBP4qDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:17:42.450584Z"},"content_sha256":"fc724d15c09ec23ce6ac9a94f087d0cf1d2cc27d4dd2c38cc0c347c64ae775ef","schema_version":"1.0","event_id":"sha256:fc724d15c09ec23ce6ac9a94f087d0cf1d2cc27d4dd2c38cc0c347c64ae775ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UUN4XIJZTWCD2FTUC7V6QFXZLX/bundle.json","state_url":"https://pith.science/pith/UUN4XIJZTWCD2FTUC7V6QFXZLX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UUN4XIJZTWCD2FTUC7V6QFXZLX/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":"2026-05-26T18:17:42Z","links":{"resolver":"https://pith.science/pith/UUN4XIJZTWCD2FTUC7V6QFXZLX","bundle":"https://pith.science/pith/UUN4XIJZTWCD2FTUC7V6QFXZLX/bundle.json","state":"https://pith.science/pith/UUN4XIJZTWCD2FTUC7V6QFXZLX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UUN4XIJZTWCD2FTUC7V6QFXZLX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UUN4XIJZTWCD2FTUC7V6QFXZLX","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":"66426f717fd45d5db64f5cb8eae68660c67a52a4930fc63d75704ee3d0086a9e","cross_cats_sorted":["cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-21T03:37:26Z","title_canon_sha256":"d0cbd99a2e567e7d3b408adc36d228eca11c3dada473c83bf7de1cfedbaabca3"},"schema_version":"1.0","source":{"id":"1801.06759","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.06759","created_at":"2026-05-18T00:24:59Z"},{"alias_kind":"arxiv_version","alias_value":"1801.06759v1","created_at":"2026-05-18T00:24:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.06759","created_at":"2026-05-18T00:24:59Z"},{"alias_kind":"pith_short_12","alias_value":"UUN4XIJZTWCD","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UUN4XIJZTWCD2FTU","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UUN4XIJZ","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:fc724d15c09ec23ce6ac9a94f087d0cf1d2cc27d4dd2c38cc0c347c64ae775ef","target":"graph","created_at":"2026-05-18T00:24:59Z","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":"Efficient computation of shortest cycles which form a homology basis under $\\mathbb{Z}_2$-additions in a given simplicial complex $\\mathcal{K}$ has been researched actively in recent years. When the complex $\\mathcal{K}$ is a weighted graph with $n$ vertices and $m$ edges, the problem of computing a shortest (homology) cycle basis is known to be solvable in $O(m^2n/\\log n+ n^2m)$-time. Several works \\cite{borradaile2017minimum, greedy} have addressed the case when the complex $\\mathcal{K}$ is a $2$-manifold. The complexity of these algorithms depends on the rank $g$ of the one-dimensional homo","authors_text":"Tamal K. Dey, Tianqi Li, Yusu Wang","cross_cats":["cs.CG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-21T03:37:26Z","title":"Efficient algorithms for computing a minimal homology basis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06759","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:cb0415bd39e3f1a2d79a8f4dac2f132c265c8e342804d22435edae8cd047b667","target":"record","created_at":"2026-05-18T00:24:59Z","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":"66426f717fd45d5db64f5cb8eae68660c67a52a4930fc63d75704ee3d0086a9e","cross_cats_sorted":["cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-21T03:37:26Z","title_canon_sha256":"d0cbd99a2e567e7d3b408adc36d228eca11c3dada473c83bf7de1cfedbaabca3"},"schema_version":"1.0","source":{"id":"1801.06759","kind":"arxiv","version":1}},"canonical_sha256":"a51bcba1399d843d167417ebe816f95dd669727123b27670b6148ff1a59c44f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a51bcba1399d843d167417ebe816f95dd669727123b27670b6148ff1a59c44f9","first_computed_at":"2026-05-18T00:24:59.142007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:59.142007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S526yAzQOY6a5H1O5cQHFKyTFY9C2giXYopiptxt4DEB5TZcc6nFeAbMYIhMX0yNOJee87FYmib0BXK9u0TqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:59.142485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.06759","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb0415bd39e3f1a2d79a8f4dac2f132c265c8e342804d22435edae8cd047b667","sha256:fc724d15c09ec23ce6ac9a94f087d0cf1d2cc27d4dd2c38cc0c347c64ae775ef"],"state_sha256":"a385e6f76f82836482340791b7d1428711a78afc42787d7e552f377af7326576"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q11VcI1ifdaLhgQcMYKY3iMjOKUq+/RyD4yVuf2vkNuOSW0rTAU2nPjGa1EcPy/6zSP793lz3EX/RDRP2eWsAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:17:42.453946Z","bundle_sha256":"50d0b59593bd5ae20905eb27bc979b4cfdda068d4332a6092ca4509e0be27d13"}}