{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:XXQSF427TY5BUOGZIQB3UCSN5K","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":"daa8e68efbe5d1f38bdecce88dca00c4c81fb3c4a73b5f9af87aa79da61573be","cross_cats_sorted":["hep-lat","math.CO"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1998-11-29T23:58:31Z","title_canon_sha256":"6f32ebf37b7f35e1d39b1550a4c38fed364653f869aad7e0999a028130edc2ea"},"schema_version":"1.0","source":{"id":"cond-mat/9811410","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9811410","created_at":"2026-05-18T01:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9811410v1","created_at":"2026-05-18T01:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9811410","created_at":"2026-05-18T01:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"XXQSF427TY5B","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"XXQSF427TY5BUOGZ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"XXQSF427","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:4b7196c4a190a3eecc65c431304b78afb8de3118b5cdc0cad8e47fbfe2299614","target":"graph","created_at":"2026-05-18T01:39:29Z","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":"We present exact calculations of the zero-temperature partition function $Z(G,q,T=0)$ and ground-state degeneracy $W(\\{G\\},q)$ for the $q$-state Potts antiferromagnet on a number of families of graphs $G$ for which (generalizing $q$ from ${\\mathbb Z}_+$ to ${\\mathbb C}$) the boundary ${\\cal B}$ of regions of analyticity of $W$ in the complex $q$ plane is noncompact, passing through $z=1/q=0$. For these types of graphs, since the reduced function $W_{red.}=q^{-1}W$ is nonanalytic at $z=0$, there is no large--$q$ Taylor series expansion of $W_{red.}$. The study of these graphs thus gives insight","authors_text":"Robert Shrock, Shan-Ho Tsai","cross_cats":["hep-lat","math.CO"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1998-11-29T23:58:31Z","title":"Ground State Entropy of Potts Antiferromagnets: Homeomorphic Classes with Noncompact W Boundaries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9811410","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:da641eb938cf95c0b0240aebc8fb5ecf25fdd24820f5a2451ab3ad98710b5fde","target":"record","created_at":"2026-05-18T01:39:29Z","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":"daa8e68efbe5d1f38bdecce88dca00c4c81fb3c4a73b5f9af87aa79da61573be","cross_cats_sorted":["hep-lat","math.CO"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1998-11-29T23:58:31Z","title_canon_sha256":"6f32ebf37b7f35e1d39b1550a4c38fed364653f869aad7e0999a028130edc2ea"},"schema_version":"1.0","source":{"id":"cond-mat/9811410","kind":"arxiv","version":1}},"canonical_sha256":"bde122f35f9e3a1a38d94403ba0a4deabab717c2944770dd1877b3c5876abf4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bde122f35f9e3a1a38d94403ba0a4deabab717c2944770dd1877b3c5876abf4f","first_computed_at":"2026-05-18T01:39:29.540027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:29.540027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gJ5jmTfaZ7bWJjyeUp50yhVDsRdi5PGOJxUgBrNWtQwYD6Y5VoUEnVjxbMNOynVqR+CeEcuvkIXc3qphcPZkDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:29.540692Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9811410","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da641eb938cf95c0b0240aebc8fb5ecf25fdd24820f5a2451ab3ad98710b5fde","sha256:4b7196c4a190a3eecc65c431304b78afb8de3118b5cdc0cad8e47fbfe2299614"],"state_sha256":"63a991d1341d38f403d578f67c411c05db01603d96f4dd83d2042d7d9c0acaa9"}