{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3MWTZBTLM3CW44KAPJMSPHIJJR","short_pith_number":"pith:3MWTZBTL","canonical_record":{"source":{"id":"1504.02822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-11T02:32:20Z","cross_cats_sorted":["hep-th","math.CO","math.GT","math.MP"],"title_canon_sha256":"7cdd8b5fa97cacc8fa4fa38f22d9ebe9af739ff6695c131d765934a847d920a4","abstract_canon_sha256":"3d4b7392d9d2e73711da403ce37be16996ea5a530a9f55d14f8570c6a98bff6e"},"schema_version":"1.0"},"canonical_sha256":"db2d3c866b66c56e71407a59279d094c7e1a486d8830b61fefcfa81d6bffd842","source":{"kind":"arxiv","id":"1504.02822","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02822","created_at":"2026-05-18T00:57:32Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02822v1","created_at":"2026-05-18T00:57:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02822","created_at":"2026-05-18T00:57:32Z"},{"alias_kind":"pith_short_12","alias_value":"3MWTZBTLM3CW","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3MWTZBTLM3CW44KA","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3MWTZBTL","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3MWTZBTLM3CW44KAPJMSPHIJJR","target":"record","payload":{"canonical_record":{"source":{"id":"1504.02822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-11T02:32:20Z","cross_cats_sorted":["hep-th","math.CO","math.GT","math.MP"],"title_canon_sha256":"7cdd8b5fa97cacc8fa4fa38f22d9ebe9af739ff6695c131d765934a847d920a4","abstract_canon_sha256":"3d4b7392d9d2e73711da403ce37be16996ea5a530a9f55d14f8570c6a98bff6e"},"schema_version":"1.0"},"canonical_sha256":"db2d3c866b66c56e71407a59279d094c7e1a486d8830b61fefcfa81d6bffd842","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:32.068493Z","signature_b64":"8mYRMb8kictHTbIJpRCQHhS5DW0jUvUeWgEzJEiZrEG7FrWVlgMM0D35l+EtQvgGLLJ7+2myIm/NHHjdVCGKBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db2d3c866b66c56e71407a59279d094c7e1a486d8830b61fefcfa81d6bffd842","last_reissued_at":"2026-05-18T00:57:32.067905Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:32.067905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.02822","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":"2026-05-18T00:57:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PMvhLGf8ZI7PWoTggykSdn2zZV0IvXuhDujpYUwZR8MuU31E5Isden4xDCpIOYGQzVfzQFo3k6mJoxKbHu8iBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:14:45.196803Z"},"content_sha256":"4e65d295bb1b33df4eedbb4553b31fce46f0ec0348697c0cc7b724ae87ccc2e2","schema_version":"1.0","event_id":"sha256:4e65d295bb1b33df4eedbb4553b31fce46f0ec0348697c0cc7b724ae87ccc2e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3MWTZBTLM3CW44KAPJMSPHIJJR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Duality between Spin networks and the 2D Ising model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CO","math.GT","math.MP"],"primary_cat":"math-ph","authors_text":"Etera R. Livine, Francesco Costantino, Valentin Bonzom","submitted_at":"2015-04-11T02:32:20Z","abstract_excerpt":"The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories which couple the geom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02822","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":"2026-05-18T00:57:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aB8zwE/luPgGFKn1tSaZ5p6jZTGveZe+0Yd6bQLkffwReK54Q1jezYRggjlDUTP70lTUBUO1bsZlcGPKZB5vAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:14:45.197478Z"},"content_sha256":"0e11c7a5d95a736c2411b04a752dd6a4c02543e72d02719d5a78b9d3ff2ae726","schema_version":"1.0","event_id":"sha256:0e11c7a5d95a736c2411b04a752dd6a4c02543e72d02719d5a78b9d3ff2ae726"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3MWTZBTLM3CW44KAPJMSPHIJJR/bundle.json","state_url":"https://pith.science/pith/3MWTZBTLM3CW44KAPJMSPHIJJR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3MWTZBTLM3CW44KAPJMSPHIJJR/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":"2026-05-27T19:14:45Z","links":{"resolver":"https://pith.science/pith/3MWTZBTLM3CW44KAPJMSPHIJJR","bundle":"https://pith.science/pith/3MWTZBTLM3CW44KAPJMSPHIJJR/bundle.json","state":"https://pith.science/pith/3MWTZBTLM3CW44KAPJMSPHIJJR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3MWTZBTLM3CW44KAPJMSPHIJJR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3MWTZBTLM3CW44KAPJMSPHIJJR","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":"3d4b7392d9d2e73711da403ce37be16996ea5a530a9f55d14f8570c6a98bff6e","cross_cats_sorted":["hep-th","math.CO","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-11T02:32:20Z","title_canon_sha256":"7cdd8b5fa97cacc8fa4fa38f22d9ebe9af739ff6695c131d765934a847d920a4"},"schema_version":"1.0","source":{"id":"1504.02822","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02822","created_at":"2026-05-18T00:57:32Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02822v1","created_at":"2026-05-18T00:57:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02822","created_at":"2026-05-18T00:57:32Z"},{"alias_kind":"pith_short_12","alias_value":"3MWTZBTLM3CW","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3MWTZBTLM3CW44KA","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3MWTZBTL","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:0e11c7a5d95a736c2411b04a752dd6a4c02543e72d02719d5a78b9d3ff2ae726","target":"graph","created_at":"2026-05-18T00:57:32Z","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":"The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories which couple the geom","authors_text":"Etera R. Livine, Francesco Costantino, Valentin Bonzom","cross_cats":["hep-th","math.CO","math.GT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-11T02:32:20Z","title":"Duality between Spin networks and the 2D Ising model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02822","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":"sha256:4e65d295bb1b33df4eedbb4553b31fce46f0ec0348697c0cc7b724ae87ccc2e2","target":"record","created_at":"2026-05-18T00:57:32Z","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":"3d4b7392d9d2e73711da403ce37be16996ea5a530a9f55d14f8570c6a98bff6e","cross_cats_sorted":["hep-th","math.CO","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-11T02:32:20Z","title_canon_sha256":"7cdd8b5fa97cacc8fa4fa38f22d9ebe9af739ff6695c131d765934a847d920a4"},"schema_version":"1.0","source":{"id":"1504.02822","kind":"arxiv","version":1}},"canonical_sha256":"db2d3c866b66c56e71407a59279d094c7e1a486d8830b61fefcfa81d6bffd842","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db2d3c866b66c56e71407a59279d094c7e1a486d8830b61fefcfa81d6bffd842","first_computed_at":"2026-05-18T00:57:32.067905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:32.067905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8mYRMb8kictHTbIJpRCQHhS5DW0jUvUeWgEzJEiZrEG7FrWVlgMM0D35l+EtQvgGLLJ7+2myIm/NHHjdVCGKBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:32.068493Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.02822","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e65d295bb1b33df4eedbb4553b31fce46f0ec0348697c0cc7b724ae87ccc2e2","sha256:0e11c7a5d95a736c2411b04a752dd6a4c02543e72d02719d5a78b9d3ff2ae726"],"state_sha256":"2e4b0f26e99d40173eb1b30c0d5bf48dcf24289bc44894de1270527edc218d69"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"avsUyMZlPeuUgez6Vc3skONZK7ilB/Cd1vrBgwxHelsTzsCTJ8C3ANd4GRuc9Cksz3mumC6Y2x81A0zw8HqtBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:14:45.201301Z","bundle_sha256":"0d9769234523f991cab1c6007cbd5573f66168b8baceac29f961a30867c5bf07"}}