{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FGSLTTOCBEELBOMWS6QV43OUPD","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":"878bfc2a487b2082cd24eb162fdf716f23c0dd243c99531396624b17fbdb9ecf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-08T13:43:04Z","title_canon_sha256":"d24f95f10fb3a8f3280a9862deba3cd7bd04dae5103b5b383f61688b4470d400"},"schema_version":"1.0","source":{"id":"1803.03086","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03086","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03086v2","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03086","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"FGSLTTOCBEEL","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FGSLTTOCBEELBOMW","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FGSLTTOC","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:83d19b204eceee53eed1911a7cb7198353f37253152fafd12d3f31b69c54a311","target":"graph","created_at":"2026-05-18T00:07:23Z","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":"This paper considers the topological degree of $G$-shifts of finite type for the case where $G$ is a nonabelian monoid. Whenever the Cayley graph of $G$ has a finite representation and the relationships among the generators of $G$ are determined by a matrix $A$, the coefficients of the characteristic polynomial of $A$ are revealed as the number of children of the graph. After introducing an algorithm for the computation of the degree, the degree spectrum, which is finite, relates to a collection of matrices in which the sum of each row of every matrix is bounded by the number of children of th","authors_text":"Chih-Hung Chang, Jung-Chao Ban, Nai-Zhu Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-08T13:43:04Z","title":"Topological Degree of Shift Spaces on Monoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03086","kind":"arxiv","version":2},"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":"sha256:7f010aadfb42e7b623ef8821353175414d8e6dc7734f773ac2df849c8ac4550a","target":"record","created_at":"2026-05-18T00:07:23Z","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":"878bfc2a487b2082cd24eb162fdf716f23c0dd243c99531396624b17fbdb9ecf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-08T13:43:04Z","title_canon_sha256":"d24f95f10fb3a8f3280a9862deba3cd7bd04dae5103b5b383f61688b4470d400"},"schema_version":"1.0","source":{"id":"1803.03086","kind":"arxiv","version":2}},"canonical_sha256":"29a4b9cdc20908b0b99697a15e6dd478cabe26ceb27eaea7c6832b3fa5d00827","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29a4b9cdc20908b0b99697a15e6dd478cabe26ceb27eaea7c6832b3fa5d00827","first_computed_at":"2026-05-18T00:07:23.607334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:23.607334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y1fequk1clB1tjGRpBGQV+P14LbVGK2vN3+YdennMysaFyNautEMgZSw1OT6kt7WMoABf7Nq4tAZQpesfC2mDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:23.607773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03086","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f010aadfb42e7b623ef8821353175414d8e6dc7734f773ac2df849c8ac4550a","sha256:83d19b204eceee53eed1911a7cb7198353f37253152fafd12d3f31b69c54a311"],"state_sha256":"98a6b91a408e85d6a8f70ac22bdc1822809ff2e1aa91590c2c42ba1caf51f7bc"}