{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GGGKOIBVRVZ7FHU5HGJMQNHEQJ","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":"3fb40647868a91a2325f694b3bcd2a349bfb7013a6e048ec1cfe6e91c034e9f4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-14T18:16:35Z","title_canon_sha256":"b586fae12f8d0561c4126f77c5d4a77845704559161e078299a367830b647e38"},"schema_version":"1.0","source":{"id":"1509.04228","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04228","created_at":"2026-05-18T01:33:08Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04228v1","created_at":"2026-05-18T01:33:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04228","created_at":"2026-05-18T01:33:08Z"},{"alias_kind":"pith_short_12","alias_value":"GGGKOIBVRVZ7","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GGGKOIBVRVZ7FHU5","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GGGKOIBV","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:a6ff12dd126bd6964bc81752314376a20f7a16a18831bbc6a0fd378a360f53e1","target":"graph","created_at":"2026-05-18T01:33:08Z","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 T be the category whose objects are rooted trees and morphisms are order embeddings preserving the root. We prove that finitely generated representations of T are Noetherian using techniques developed by Sam and Snowden which generalize classical Grobner theory. The proof uses a relative version of Kruskals tree Theorem.","authors_text":"Daniel Barter","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-14T18:16:35Z","title":"Noetherianity and rooted trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04228","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:d1e31e4bf58a51c771b52c009dd274dae756daa84cde59997e95cd276121d7d2","target":"record","created_at":"2026-05-18T01:33:08Z","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":"3fb40647868a91a2325f694b3bcd2a349bfb7013a6e048ec1cfe6e91c034e9f4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-14T18:16:35Z","title_canon_sha256":"b586fae12f8d0561c4126f77c5d4a77845704559161e078299a367830b647e38"},"schema_version":"1.0","source":{"id":"1509.04228","kind":"arxiv","version":1}},"canonical_sha256":"318ca720358d73f29e9d3992c834e48241ff1062090e40699ff6fed541a3a7eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"318ca720358d73f29e9d3992c834e48241ff1062090e40699ff6fed541a3a7eb","first_computed_at":"2026-05-18T01:33:08.017689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:08.017689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u9Gi60Zyygft/cVj2AI2j74/nDpzk3yeX0rgmakEaIjiYFH9Q4h9u3l29X6skafwih9Bos6zYZbItsWnOW5ODg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:08.018459Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.04228","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1e31e4bf58a51c771b52c009dd274dae756daa84cde59997e95cd276121d7d2","sha256:a6ff12dd126bd6964bc81752314376a20f7a16a18831bbc6a0fd378a360f53e1"],"state_sha256":"e0508db4f937d5622fdfdbed764c8b2721e0043bcb458c5394ef66a88072416d"}