{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7Y6CGUZA2DDSS5UM7YIOUD765L","short_pith_number":"pith:7Y6CGUZA","canonical_record":{"source":{"id":"1605.02915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-10T10:02:06Z","cross_cats_sorted":["cond-mat.stat-mech","math.CA","math.MP"],"title_canon_sha256":"4cb85333ee0c7d336a41a6b63adce0ba9bc239e7a12fbdd02eec6b490997b608","abstract_canon_sha256":"ae18b439900d838fa2a002fcb09d53fb88e04d2811630d31017a4383c5046947"},"schema_version":"1.0"},"canonical_sha256":"fe3c235320d0c729768cfe10ea0ffeeafe99246ff0403872f0322d37663d16bc","source":{"kind":"arxiv","id":"1605.02915","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02915","created_at":"2026-05-18T01:04:20Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02915v1","created_at":"2026-05-18T01:04:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02915","created_at":"2026-05-18T01:04:20Z"},{"alias_kind":"pith_short_12","alias_value":"7Y6CGUZA2DDS","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7Y6CGUZA2DDSS5UM","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7Y6CGUZA","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7Y6CGUZA2DDSS5UM7YIOUD765L","target":"record","payload":{"canonical_record":{"source":{"id":"1605.02915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-10T10:02:06Z","cross_cats_sorted":["cond-mat.stat-mech","math.CA","math.MP"],"title_canon_sha256":"4cb85333ee0c7d336a41a6b63adce0ba9bc239e7a12fbdd02eec6b490997b608","abstract_canon_sha256":"ae18b439900d838fa2a002fcb09d53fb88e04d2811630d31017a4383c5046947"},"schema_version":"1.0"},"canonical_sha256":"fe3c235320d0c729768cfe10ea0ffeeafe99246ff0403872f0322d37663d16bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:20.472423Z","signature_b64":"JQkbBP6qju/3DaNaDdNOR1uB/h42t83yUYZHcKP9fmTahtqToALuq1gfLAIkuK0WtzNq6AdRMCl6jkmQ5gGTCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe3c235320d0c729768cfe10ea0ffeeafe99246ff0403872f0322d37663d16bc","last_reissued_at":"2026-05-18T01:04:20.471857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:20.471857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.02915","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":"2026-05-18T01:04:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Si6LlXBxrn3Ec747V8k+FKPiIuagrMbJc6X6QRL8T1X/Ua0SMbwpLCJP+hMQUjUamawIenA+o4BQ5P6uqqGbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T16:42:39.360629Z"},"content_sha256":"f2ddf7158ea2a537d198811c07a8216ddb0a3c16dfd30953b5956f178fd4c38a","schema_version":"1.0","event_id":"sha256:f2ddf7158ea2a537d198811c07a8216ddb0a3c16dfd30953b5956f178fd4c38a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7Y6CGUZA2DDSS5UM7YIOUD765L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elliptic pfaffians and solvable lattice models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Hjalmar Rosengren","submitted_at":"2016-05-10T10:02:06Z","abstract_excerpt":"We introduce and study twelve multivariable theta functions defined by pfaffians with elliptic function entries. We show that, when the crossing parameter is a cubic root of unity, the domain wall partition function for the eight-vertex-solid-on-solid model can be written as a sum of two of these pfaffians. As a limit case, we express the domain wall partition function for the three-colour model as a sum of two Hankel determinants. We also show that certain solutions of the TQ-equation for the supersymmetric eight-vertex model can be expressed in terms of elliptic pfaffians."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02915","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":"2026-05-18T01:04:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZobpHHlMU6jky7N2HArB/WUPw8AL6aJ3kTbJ8OZxAgLfuBGa6A5Kp/itbPDt/xW7Xqn0BmgOGswNDCSv8+e9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T16:42:39.361394Z"},"content_sha256":"3d6205c1d8b63b6612e11f64ff38f7da6ae5263c807f20b5a5a4ff0f549953b4","schema_version":"1.0","event_id":"sha256:3d6205c1d8b63b6612e11f64ff38f7da6ae5263c807f20b5a5a4ff0f549953b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7Y6CGUZA2DDSS5UM7YIOUD765L/bundle.json","state_url":"https://pith.science/pith/7Y6CGUZA2DDSS5UM7YIOUD765L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7Y6CGUZA2DDSS5UM7YIOUD765L/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":"2026-05-23T16:42:39Z","links":{"resolver":"https://pith.science/pith/7Y6CGUZA2DDSS5UM7YIOUD765L","bundle":"https://pith.science/pith/7Y6CGUZA2DDSS5UM7YIOUD765L/bundle.json","state":"https://pith.science/pith/7Y6CGUZA2DDSS5UM7YIOUD765L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7Y6CGUZA2DDSS5UM7YIOUD765L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7Y6CGUZA2DDSS5UM7YIOUD765L","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":"ae18b439900d838fa2a002fcb09d53fb88e04d2811630d31017a4383c5046947","cross_cats_sorted":["cond-mat.stat-mech","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-10T10:02:06Z","title_canon_sha256":"4cb85333ee0c7d336a41a6b63adce0ba9bc239e7a12fbdd02eec6b490997b608"},"schema_version":"1.0","source":{"id":"1605.02915","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02915","created_at":"2026-05-18T01:04:20Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02915v1","created_at":"2026-05-18T01:04:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02915","created_at":"2026-05-18T01:04:20Z"},{"alias_kind":"pith_short_12","alias_value":"7Y6CGUZA2DDS","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7Y6CGUZA2DDSS5UM","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7Y6CGUZA","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:3d6205c1d8b63b6612e11f64ff38f7da6ae5263c807f20b5a5a4ff0f549953b4","target":"graph","created_at":"2026-05-18T01:04:20Z","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 introduce and study twelve multivariable theta functions defined by pfaffians with elliptic function entries. We show that, when the crossing parameter is a cubic root of unity, the domain wall partition function for the eight-vertex-solid-on-solid model can be written as a sum of two of these pfaffians. As a limit case, we express the domain wall partition function for the three-colour model as a sum of two Hankel determinants. We also show that certain solutions of the TQ-equation for the supersymmetric eight-vertex model can be expressed in terms of elliptic pfaffians.","authors_text":"Hjalmar Rosengren","cross_cats":["cond-mat.stat-mech","math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-10T10:02:06Z","title":"Elliptic pfaffians and solvable lattice models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02915","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:f2ddf7158ea2a537d198811c07a8216ddb0a3c16dfd30953b5956f178fd4c38a","target":"record","created_at":"2026-05-18T01:04:20Z","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":"ae18b439900d838fa2a002fcb09d53fb88e04d2811630d31017a4383c5046947","cross_cats_sorted":["cond-mat.stat-mech","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-10T10:02:06Z","title_canon_sha256":"4cb85333ee0c7d336a41a6b63adce0ba9bc239e7a12fbdd02eec6b490997b608"},"schema_version":"1.0","source":{"id":"1605.02915","kind":"arxiv","version":1}},"canonical_sha256":"fe3c235320d0c729768cfe10ea0ffeeafe99246ff0403872f0322d37663d16bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe3c235320d0c729768cfe10ea0ffeeafe99246ff0403872f0322d37663d16bc","first_computed_at":"2026-05-18T01:04:20.471857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:20.471857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JQkbBP6qju/3DaNaDdNOR1uB/h42t83yUYZHcKP9fmTahtqToALuq1gfLAIkuK0WtzNq6AdRMCl6jkmQ5gGTCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:20.472423Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.02915","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2ddf7158ea2a537d198811c07a8216ddb0a3c16dfd30953b5956f178fd4c38a","sha256:3d6205c1d8b63b6612e11f64ff38f7da6ae5263c807f20b5a5a4ff0f549953b4"],"state_sha256":"9a34cc85100fa28d621dcb31dc772b91bdfe543b7d1c8716f0d200de0265c999"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jOk/Tw5MPDcK0kXNzxDm/uUQDsAWyES/a/74E7JPcJiszCM7nESOOYSsMcJxcvrIV28FnwHeQFKJg3YSiKh0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T16:42:39.365060Z","bundle_sha256":"7630f3615e03e5d222bd2190a47f78fa03c73a37ed7d659c7a6ea9f26160896f"}}