{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JTGUIAGWKA6B5TDM33GUPGBUDC","short_pith_number":"pith:JTGUIAGW","canonical_record":{"source":{"id":"1207.5862","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-25T01:16:02Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"21c249c058e83e7dec5b5f58d21dafb315c04d9175a0e50a36e9b364eaa21916","abstract_canon_sha256":"eb626527f65516ad347eb4e4eefa6c0e49aba2d49e55570316e5334b35de107e"},"schema_version":"1.0"},"canonical_sha256":"4ccd4400d6503c1ecc6cdecd47983418bc7411e4a05e8aabb970b8a587778adc","source":{"kind":"arxiv","id":"1207.5862","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5862","created_at":"2026-05-18T03:50:10Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5862v1","created_at":"2026-05-18T03:50:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5862","created_at":"2026-05-18T03:50:10Z"},{"alias_kind":"pith_short_12","alias_value":"JTGUIAGWKA6B","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JTGUIAGWKA6B5TDM","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JTGUIAGW","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JTGUIAGWKA6B5TDM33GUPGBUDC","target":"record","payload":{"canonical_record":{"source":{"id":"1207.5862","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-25T01:16:02Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"21c249c058e83e7dec5b5f58d21dafb315c04d9175a0e50a36e9b364eaa21916","abstract_canon_sha256":"eb626527f65516ad347eb4e4eefa6c0e49aba2d49e55570316e5334b35de107e"},"schema_version":"1.0"},"canonical_sha256":"4ccd4400d6503c1ecc6cdecd47983418bc7411e4a05e8aabb970b8a587778adc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:10.114417Z","signature_b64":"jZk1NprIbZlN8aOnxiACOl2PWmytvm1Lp+qOI/sNoC/q3hu8ztRVYWdnbTDy4Q9rSnMGo34f8OlPmr0DDvl1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ccd4400d6503c1ecc6cdecd47983418bc7411e4a05e8aabb970b8a587778adc","last_reissued_at":"2026-05-18T03:50:10.113563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:10.113563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.5862","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":"2026-05-18T03:50:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+x8E5Y8TQuID5EbvR7aogfSpB3M0I+V505LLYvthcAjyBzrOMtsnj02wDnOML+ZItZSZPWI/UrtzyQksjIQMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:50:26.398830Z"},"content_sha256":"88a7c1b447b803bfc7d799ee61ff25bf4589d1c3f293d906f4fafd1ad9f0e665","schema_version":"1.0","event_id":"sha256:88a7c1b447b803bfc7d799ee61ff25bf4589d1c3f293d906f4fafd1ad9f0e665"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JTGUIAGWKA6B5TDM33GUPGBUDC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homology of Homogeneous Divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Aron Simis, Stefan O. Tohaneanu","submitted_at":"2012-07-25T01:16:02Z","abstract_excerpt":"One deals with arbitrary reduced free divisors in a polynomial ring over a field of characteristic zero, by stressing the ideal theoretic and homological behavior of the corresponding singular locus. A particular emphasis is given to both weighted homogeneous and homogeneous polynomials, allowing to introduce new families of free divisors which do not come from hyperplane arrangements nor as explicit discriminants from singularity theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5862","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":"2026-05-18T03:50:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3FDPAY9eogkX+i/40tugSLKAvlRh8yZ9d9S12Iw/8s+5g6+AftWUk73D9S3kM78yTigerHsl3ZWWE1BDLC7TDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:50:26.399165Z"},"content_sha256":"9f456186f56b1ac0057766663c1a533775087c9e4dae6ac63a12abe4321b2417","schema_version":"1.0","event_id":"sha256:9f456186f56b1ac0057766663c1a533775087c9e4dae6ac63a12abe4321b2417"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JTGUIAGWKA6B5TDM33GUPGBUDC/bundle.json","state_url":"https://pith.science/pith/JTGUIAGWKA6B5TDM33GUPGBUDC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JTGUIAGWKA6B5TDM33GUPGBUDC/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":"2026-06-25T08:50:26Z","links":{"resolver":"https://pith.science/pith/JTGUIAGWKA6B5TDM33GUPGBUDC","bundle":"https://pith.science/pith/JTGUIAGWKA6B5TDM33GUPGBUDC/bundle.json","state":"https://pith.science/pith/JTGUIAGWKA6B5TDM33GUPGBUDC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JTGUIAGWKA6B5TDM33GUPGBUDC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JTGUIAGWKA6B5TDM33GUPGBUDC","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":"eb626527f65516ad347eb4e4eefa6c0e49aba2d49e55570316e5334b35de107e","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-25T01:16:02Z","title_canon_sha256":"21c249c058e83e7dec5b5f58d21dafb315c04d9175a0e50a36e9b364eaa21916"},"schema_version":"1.0","source":{"id":"1207.5862","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5862","created_at":"2026-05-18T03:50:10Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5862v1","created_at":"2026-05-18T03:50:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5862","created_at":"2026-05-18T03:50:10Z"},{"alias_kind":"pith_short_12","alias_value":"JTGUIAGWKA6B","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JTGUIAGWKA6B5TDM","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JTGUIAGW","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:9f456186f56b1ac0057766663c1a533775087c9e4dae6ac63a12abe4321b2417","target":"graph","created_at":"2026-05-18T03:50:10Z","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":"One deals with arbitrary reduced free divisors in a polynomial ring over a field of characteristic zero, by stressing the ideal theoretic and homological behavior of the corresponding singular locus. A particular emphasis is given to both weighted homogeneous and homogeneous polynomials, allowing to introduce new families of free divisors which do not come from hyperplane arrangements nor as explicit discriminants from singularity theory.","authors_text":"Aron Simis, Stefan O. Tohaneanu","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-25T01:16:02Z","title":"Homology of Homogeneous Divisors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5862","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":"sha256:88a7c1b447b803bfc7d799ee61ff25bf4589d1c3f293d906f4fafd1ad9f0e665","target":"record","created_at":"2026-05-18T03:50:10Z","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":"eb626527f65516ad347eb4e4eefa6c0e49aba2d49e55570316e5334b35de107e","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-25T01:16:02Z","title_canon_sha256":"21c249c058e83e7dec5b5f58d21dafb315c04d9175a0e50a36e9b364eaa21916"},"schema_version":"1.0","source":{"id":"1207.5862","kind":"arxiv","version":1}},"canonical_sha256":"4ccd4400d6503c1ecc6cdecd47983418bc7411e4a05e8aabb970b8a587778adc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ccd4400d6503c1ecc6cdecd47983418bc7411e4a05e8aabb970b8a587778adc","first_computed_at":"2026-05-18T03:50:10.113563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:10.113563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jZk1NprIbZlN8aOnxiACOl2PWmytvm1Lp+qOI/sNoC/q3hu8ztRVYWdnbTDy4Q9rSnMGo34f8OlPmr0DDvl1BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:10.114417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5862","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88a7c1b447b803bfc7d799ee61ff25bf4589d1c3f293d906f4fafd1ad9f0e665","sha256:9f456186f56b1ac0057766663c1a533775087c9e4dae6ac63a12abe4321b2417"],"state_sha256":"9b014e7171bdc69b2a5de5eb558569048edcf13b1441b8c9cd3f70d3ac32b9a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HGZ0sHaOjq6XC2+WLU1qscEYTPCClnaUMc7U91c4VDIGDNSAVIaJb8OWDuvmURgRevg4DPVplnvcLLM0c1MmDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:50:26.401008Z","bundle_sha256":"d35b6271eca60ad944fbe3c2ef4126734df5567af95db546778cb66ff7a5f96c"}}