{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OQ2RYEIHY4D7HXMXWGJFXOKGZC","short_pith_number":"pith:OQ2RYEIH","canonical_record":{"source":{"id":"1412.2561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-08T13:55:14Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"cecfb2036f63b5b7a56ea1968b01dbb646755ff5c1a72e651e70d4dfd74135e2","abstract_canon_sha256":"4baae86c73974114d19a1ce3b08e64549eaea2a9be6baf866b2974f4e8b91fc2"},"schema_version":"1.0"},"canonical_sha256":"74351c1107c707f3dd97b1925bb946c89428fd1f6e4999c3458d92677d93070b","source":{"kind":"arxiv","id":"1412.2561","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2561","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2561v1","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2561","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"pith_short_12","alias_value":"OQ2RYEIHY4D7","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OQ2RYEIHY4D7HXMX","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OQ2RYEIH","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OQ2RYEIHY4D7HXMXWGJFXOKGZC","target":"record","payload":{"canonical_record":{"source":{"id":"1412.2561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-08T13:55:14Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"cecfb2036f63b5b7a56ea1968b01dbb646755ff5c1a72e651e70d4dfd74135e2","abstract_canon_sha256":"4baae86c73974114d19a1ce3b08e64549eaea2a9be6baf866b2974f4e8b91fc2"},"schema_version":"1.0"},"canonical_sha256":"74351c1107c707f3dd97b1925bb946c89428fd1f6e4999c3458d92677d93070b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:57.591481Z","signature_b64":"H+4+K1ROmzcqZ6n+7trwBdNjPQCeH71gInWjJ73Dyrz20nTP31tZ+uDrB3EsW7dTk1N+dVx0wExNwgiRcURUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74351c1107c707f3dd97b1925bb946c89428fd1f6e4999c3458d92677d93070b","last_reissued_at":"2026-05-18T02:31:57.590689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:57.590689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.2561","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":"2026-05-18T02:31:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O7z0BHVaS/dcP5W6AoulaH/JLIEXtgv4lOxVDPYz+wflud2h+HLCyv4PQMgLD/j37CIpUhyaPAWkHFdGQjlyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:37:49.821833Z"},"content_sha256":"bd81927117365192bca9753fb9d1b5e4039867a379cbfe334a0ea9c5b447b9d3","schema_version":"1.0","event_id":"sha256:bd81927117365192bca9753fb9d1b5e4039867a379cbfe334a0ea9c5b447b9d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OQ2RYEIHY4D7HXMXWGJFXOKGZC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On commutative algebra associated to $t$-labeled subforests of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Gleb Nenashev","submitted_at":"2014-12-08T13:55:14Z","abstract_excerpt":"For a given graph $G$, we construct an associated commutative algebra, whose dimension is equal to the number of $t$-labeled forests of $G$.\n  We show that the dimension of the $k$-th graded component of this algebra also has a combinatorial meaning and that its Hilbert polynomial can be expressed through the Tutte polynomial of $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2561","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":"2026-05-18T02:31:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qxMS8UnVDNwlf9zHw/2T3OhmCuuHWdGwGrt7KlBvgYjSn6eb+7U1T9z/mkkZxXvlfDn+fBCIOrhldecuelu2Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:37:49.822423Z"},"content_sha256":"17f1be4feeba22d43dcfdd1d474f9f4fc6fb1cfed38af82d70dd209ab3ec8291","schema_version":"1.0","event_id":"sha256:17f1be4feeba22d43dcfdd1d474f9f4fc6fb1cfed38af82d70dd209ab3ec8291"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OQ2RYEIHY4D7HXMXWGJFXOKGZC/bundle.json","state_url":"https://pith.science/pith/OQ2RYEIHY4D7HXMXWGJFXOKGZC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OQ2RYEIHY4D7HXMXWGJFXOKGZC/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":"2026-05-27T16:37:49Z","links":{"resolver":"https://pith.science/pith/OQ2RYEIHY4D7HXMXWGJFXOKGZC","bundle":"https://pith.science/pith/OQ2RYEIHY4D7HXMXWGJFXOKGZC/bundle.json","state":"https://pith.science/pith/OQ2RYEIHY4D7HXMXWGJFXOKGZC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OQ2RYEIHY4D7HXMXWGJFXOKGZC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OQ2RYEIHY4D7HXMXWGJFXOKGZC","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":"4baae86c73974114d19a1ce3b08e64549eaea2a9be6baf866b2974f4e8b91fc2","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-08T13:55:14Z","title_canon_sha256":"cecfb2036f63b5b7a56ea1968b01dbb646755ff5c1a72e651e70d4dfd74135e2"},"schema_version":"1.0","source":{"id":"1412.2561","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2561","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2561v1","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2561","created_at":"2026-05-18T02:31:57Z"},{"alias_kind":"pith_short_12","alias_value":"OQ2RYEIHY4D7","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OQ2RYEIHY4D7HXMX","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OQ2RYEIH","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:17f1be4feeba22d43dcfdd1d474f9f4fc6fb1cfed38af82d70dd209ab3ec8291","target":"graph","created_at":"2026-05-18T02:31:57Z","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":"For a given graph $G$, we construct an associated commutative algebra, whose dimension is equal to the number of $t$-labeled forests of $G$.\n  We show that the dimension of the $k$-th graded component of this algebra also has a combinatorial meaning and that its Hilbert polynomial can be expressed through the Tutte polynomial of $G$.","authors_text":"Gleb Nenashev","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-08T13:55:14Z","title":"On commutative algebra associated to $t$-labeled subforests of a graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2561","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:bd81927117365192bca9753fb9d1b5e4039867a379cbfe334a0ea9c5b447b9d3","target":"record","created_at":"2026-05-18T02:31:57Z","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":"4baae86c73974114d19a1ce3b08e64549eaea2a9be6baf866b2974f4e8b91fc2","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-08T13:55:14Z","title_canon_sha256":"cecfb2036f63b5b7a56ea1968b01dbb646755ff5c1a72e651e70d4dfd74135e2"},"schema_version":"1.0","source":{"id":"1412.2561","kind":"arxiv","version":1}},"canonical_sha256":"74351c1107c707f3dd97b1925bb946c89428fd1f6e4999c3458d92677d93070b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74351c1107c707f3dd97b1925bb946c89428fd1f6e4999c3458d92677d93070b","first_computed_at":"2026-05-18T02:31:57.590689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:57.590689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H+4+K1ROmzcqZ6n+7trwBdNjPQCeH71gInWjJ73Dyrz20nTP31tZ+uDrB3EsW7dTk1N+dVx0wExNwgiRcURUDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:57.591481Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2561","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd81927117365192bca9753fb9d1b5e4039867a379cbfe334a0ea9c5b447b9d3","sha256:17f1be4feeba22d43dcfdd1d474f9f4fc6fb1cfed38af82d70dd209ab3ec8291"],"state_sha256":"e683a3b4d3c5dd07109f45625a7f2ffbb430ba93c1baaf0a0a390430640293f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"su97719iTNdktz0q5OoYe2LKoxsudtwWk05k5ZpmwSPwlr4U2RP4U3GCVy5vfbwnpXXUCvXZIbn4o3brxG6MDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T16:37:49.825144Z","bundle_sha256":"fcb75ceafef1f7fea259858590960e6182b1d7d08fd0127bf34029a2dabfde58"}}