{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:BZJ4VASBTZLY6E3OE5NTIYZJUC","short_pith_number":"pith:BZJ4VASB","canonical_record":{"source":{"id":"1110.2507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-11T20:43:04Z","cross_cats_sorted":[],"title_canon_sha256":"5d252c197aea75729563e0d10c0f69623a5bbf400ca97555eae611430cfdf166","abstract_canon_sha256":"50c37100829459c027d7af3ac2e34b57345381c572fc81fd0ac17fe2cbdc2e0c"},"schema_version":"1.0"},"canonical_sha256":"0e53ca82419e578f136e275b346329a08c4a625aeb271d6feed9cc0f000970c0","source":{"kind":"arxiv","id":"1110.2507","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2507","created_at":"2026-05-18T04:11:08Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2507v1","created_at":"2026-05-18T04:11:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2507","created_at":"2026-05-18T04:11:08Z"},{"alias_kind":"pith_short_12","alias_value":"BZJ4VASBTZLY","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BZJ4VASBTZLY6E3O","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BZJ4VASB","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:BZJ4VASBTZLY6E3OE5NTIYZJUC","target":"record","payload":{"canonical_record":{"source":{"id":"1110.2507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-11T20:43:04Z","cross_cats_sorted":[],"title_canon_sha256":"5d252c197aea75729563e0d10c0f69623a5bbf400ca97555eae611430cfdf166","abstract_canon_sha256":"50c37100829459c027d7af3ac2e34b57345381c572fc81fd0ac17fe2cbdc2e0c"},"schema_version":"1.0"},"canonical_sha256":"0e53ca82419e578f136e275b346329a08c4a625aeb271d6feed9cc0f000970c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:08.738015Z","signature_b64":"XlmikmR4B1Qvy+p3a6o7HhSkwct9wUyol8XoOl2+C0+nkGWMzQ+CY1ZscwBchrX2w5ZHHg8+ozyqopoZuM9ECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e53ca82419e578f136e275b346329a08c4a625aeb271d6feed9cc0f000970c0","last_reissued_at":"2026-05-18T04:11:08.737377Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:08.737377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.2507","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":"2026-05-18T04:11:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8aLHM3IGBnmANs1nuPoj5qIQhGA8J3wDGUMZuuxX2M9QXmIvqScAm5LEXkfvgl+huFqnm+iwsCkFKm2Vpo4lBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:42:30.148202Z"},"content_sha256":"083ec85348c3e721b9dee2599aa90ac28ada5b416ad9831d590fc4ba4a949ab9","schema_version":"1.0","event_id":"sha256:083ec85348c3e721b9dee2599aa90ac28ada5b416ad9831d590fc4ba4a949ab9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:BZJ4VASBTZLY6E3OE5NTIYZJUC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-degenerated groundstates in the antiferromagnetic Ising model on triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrea Jim\\'enez","submitted_at":"2011-10-11T20:43:04Z","abstract_excerpt":"A triangulation is an embedding of a graph into a closed Riemann surface so that each face boundary is a 3-cycle of the graph. In this work, groundstate degeneracy in the antiferromagnetic Ising model on triangulations is studied. We show that for every fixed closed Riemann surface S, there are vertex-increasing sequences of triangulations of S with a non-degenerated groundstate. In particular, we exhibit geometrically frustrated systems with a non-degenerated groundstate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2507","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":"2026-05-18T04:11:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mHV7BctRgHFMpjMgDz01gpOw5lNskyI9yY30ylcPmVb/kYU/SQw4Noc3bL+K7FFHwVZ9Ud9wU2ti/FYDgaKYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:42:30.148560Z"},"content_sha256":"6bcaf8a2d5ed1ea9f1673167a86d58b46fcb4da72549d031d27405ea2099c1ac","schema_version":"1.0","event_id":"sha256:6bcaf8a2d5ed1ea9f1673167a86d58b46fcb4da72549d031d27405ea2099c1ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BZJ4VASBTZLY6E3OE5NTIYZJUC/bundle.json","state_url":"https://pith.science/pith/BZJ4VASBTZLY6E3OE5NTIYZJUC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BZJ4VASBTZLY6E3OE5NTIYZJUC/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":"2026-06-23T21:42:30Z","links":{"resolver":"https://pith.science/pith/BZJ4VASBTZLY6E3OE5NTIYZJUC","bundle":"https://pith.science/pith/BZJ4VASBTZLY6E3OE5NTIYZJUC/bundle.json","state":"https://pith.science/pith/BZJ4VASBTZLY6E3OE5NTIYZJUC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BZJ4VASBTZLY6E3OE5NTIYZJUC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BZJ4VASBTZLY6E3OE5NTIYZJUC","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":"50c37100829459c027d7af3ac2e34b57345381c572fc81fd0ac17fe2cbdc2e0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-11T20:43:04Z","title_canon_sha256":"5d252c197aea75729563e0d10c0f69623a5bbf400ca97555eae611430cfdf166"},"schema_version":"1.0","source":{"id":"1110.2507","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2507","created_at":"2026-05-18T04:11:08Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2507v1","created_at":"2026-05-18T04:11:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2507","created_at":"2026-05-18T04:11:08Z"},{"alias_kind":"pith_short_12","alias_value":"BZJ4VASBTZLY","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BZJ4VASBTZLY6E3O","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BZJ4VASB","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:6bcaf8a2d5ed1ea9f1673167a86d58b46fcb4da72549d031d27405ea2099c1ac","target":"graph","created_at":"2026-05-18T04:11:08Z","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":"A triangulation is an embedding of a graph into a closed Riemann surface so that each face boundary is a 3-cycle of the graph. In this work, groundstate degeneracy in the antiferromagnetic Ising model on triangulations is studied. We show that for every fixed closed Riemann surface S, there are vertex-increasing sequences of triangulations of S with a non-degenerated groundstate. In particular, we exhibit geometrically frustrated systems with a non-degenerated groundstate.","authors_text":"Andrea Jim\\'enez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-11T20:43:04Z","title":"Non-degenerated groundstates in the antiferromagnetic Ising model on triangulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2507","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":"sha256:083ec85348c3e721b9dee2599aa90ac28ada5b416ad9831d590fc4ba4a949ab9","target":"record","created_at":"2026-05-18T04:11:08Z","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":"50c37100829459c027d7af3ac2e34b57345381c572fc81fd0ac17fe2cbdc2e0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-11T20:43:04Z","title_canon_sha256":"5d252c197aea75729563e0d10c0f69623a5bbf400ca97555eae611430cfdf166"},"schema_version":"1.0","source":{"id":"1110.2507","kind":"arxiv","version":1}},"canonical_sha256":"0e53ca82419e578f136e275b346329a08c4a625aeb271d6feed9cc0f000970c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e53ca82419e578f136e275b346329a08c4a625aeb271d6feed9cc0f000970c0","first_computed_at":"2026-05-18T04:11:08.737377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:08.737377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XlmikmR4B1Qvy+p3a6o7HhSkwct9wUyol8XoOl2+C0+nkGWMzQ+CY1ZscwBchrX2w5ZHHg8+ozyqopoZuM9ECw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:08.738015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2507","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:083ec85348c3e721b9dee2599aa90ac28ada5b416ad9831d590fc4ba4a949ab9","sha256:6bcaf8a2d5ed1ea9f1673167a86d58b46fcb4da72549d031d27405ea2099c1ac"],"state_sha256":"73002cc4534475e55182d18b2840334aae88dff73d5e8e0f8cafca435e66f144"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nu1ChyQZY3VcxPgEybb3G31s7XnjvBSc7nvITPNrFriNX+YH1m+FuD39uOvwZFx2o3DhSlieK42fb+Hv3d9nBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T21:42:30.150568Z","bundle_sha256":"c6b93281243efcbb3393c0dff4729d37194c386ddcffb0e3e4c83742388f89fb"}}