{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AVEHMA3JBONCIZ7PDER2IEX6AK","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":"55b8b318b228c78793ff9d46ca9143a68ba75f5e43cee1616bab0e37bfa11049","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-12-02T17:04:13Z","title_canon_sha256":"78a971f408f45f453fdb7aeb69fb3d19c1ded857596271f30a750dd9b247ba98"},"schema_version":"1.0","source":{"id":"1612.00749","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00749","created_at":"2026-05-17T23:52:56Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00749v5","created_at":"2026-05-17T23:52:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00749","created_at":"2026-05-17T23:52:56Z"},{"alias_kind":"pith_short_12","alias_value":"AVEHMA3JBONC","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AVEHMA3JBONCIZ7P","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AVEHMA3J","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:090d9401915d685e7457597988b3d5690c12cba8f9c2c769dabba785042f48d2","target":"graph","created_at":"2026-05-17T23:52:56Z","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":"Let $A$ be a commutative noetherian ring, containing a field $k$, with $1/2\\in k$, $\\dim A=d$, and let $P$ be a projective $A$-module or $rank(P)=n$. In continuation of \\cite{MM}, we study Homotopy obstructions for $P$ to split off a free direct summand. Let ${\\mathcal LO}(P)$ be the set of all pairs $(I, \\omega)$, where $I$ is an ideal of $A$ and $\\omega: P\\rightarrow I/I^2$ is a surjective map. The homotopy relations on ${\\mathcal LO}(P)$, induced by ${\\mathcal LO}(P[T])$, leads to a set $\\pi_0\\left({\\mathcal LO}(P)\\right)$ of equivalence classes in ${\\mathcal LO}(P)$. There are two distingu","authors_text":"Bibekananda Mishra, Satya Mandal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-12-02T17:04:13Z","title":"The Monoid Structure on Homotopy Obstructions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00749","kind":"arxiv","version":5},"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":"sha256:485683ed1f0443b056ee04c6b4c4095dce7f7ea1b271144ca3ff2f862a26fd55","target":"record","created_at":"2026-05-17T23:52:56Z","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":"55b8b318b228c78793ff9d46ca9143a68ba75f5e43cee1616bab0e37bfa11049","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-12-02T17:04:13Z","title_canon_sha256":"78a971f408f45f453fdb7aeb69fb3d19c1ded857596271f30a750dd9b247ba98"},"schema_version":"1.0","source":{"id":"1612.00749","kind":"arxiv","version":5}},"canonical_sha256":"05487603690b9a2467ef1923a412fe02a487204ef116335c3b9891c52dcb74b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05487603690b9a2467ef1923a412fe02a487204ef116335c3b9891c52dcb74b5","first_computed_at":"2026-05-17T23:52:56.285191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:56.285191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GcotB7wYEwBhDmugXjgQSxGNMf+idqkhApAzDZ+V0jnbC9EIxA4DxSDzUdBcV1dr6LLVWbMNv7ugWQS1pVCjCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:56.285962Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.00749","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:485683ed1f0443b056ee04c6b4c4095dce7f7ea1b271144ca3ff2f862a26fd55","sha256:090d9401915d685e7457597988b3d5690c12cba8f9c2c769dabba785042f48d2"],"state_sha256":"6b6969c560c1d2d44a328acfc55bbef0f292d44a8d3eeac2ab63be28d8f05003"}