{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:UTHEUF2KPEAJXJGYAH52J5KS4Y","short_pith_number":"pith:UTHEUF2K","canonical_record":{"source":{"id":"math/0506542","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2005-06-27T14:37:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9974f2715199c1074d272a80da5cfc6e1dd8611b5fa19e1bf860f0a3102f8799","abstract_canon_sha256":"2c190a4dd86977088e3d9e0b25b2eada0956cc1fa20ed9bffa3809191ce76f84"},"schema_version":"1.0"},"canonical_sha256":"a4ce4a174a79009ba4d801fba4f552e614cb10937b5ad113b5611e12b2a456f4","source":{"kind":"arxiv","id":"math/0506542","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0506542","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0506542v1","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506542","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"UTHEUF2KPEAJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"UTHEUF2KPEAJXJGY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"UTHEUF2K","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:UTHEUF2KPEAJXJGYAH52J5KS4Y","target":"record","payload":{"canonical_record":{"source":{"id":"math/0506542","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2005-06-27T14:37:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9974f2715199c1074d272a80da5cfc6e1dd8611b5fa19e1bf860f0a3102f8799","abstract_canon_sha256":"2c190a4dd86977088e3d9e0b25b2eada0956cc1fa20ed9bffa3809191ce76f84"},"schema_version":"1.0"},"canonical_sha256":"a4ce4a174a79009ba4d801fba4f552e614cb10937b5ad113b5611e12b2a456f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:23.365245Z","signature_b64":"WReBBM4K0r7cS6dIWg69RUA5iDQUXJMwterf9MPFDhf415obRaRk8nexi34asTIfSPUGKiQ9FCdIGT6ZpPHZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4ce4a174a79009ba4d801fba4f552e614cb10937b5ad113b5611e12b2a456f4","last_reissued_at":"2026-05-18T01:05:23.364745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:23.364745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0506542","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":"2026-05-18T01:05:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tvcaA81zWXM14n4pMLJaiePanvDBYMNZOmXx5gMeMGsW65PYkwfE+woGFUnsHXJ7dcH0iT2DP75IOdrrRbP9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:08:23.451955Z"},"content_sha256":"ba1ac69368d75925a04a2fc23efeb865d63e944a964495be11b57163269a870d","schema_version":"1.0","event_id":"sha256:ba1ac69368d75925a04a2fc23efeb865d63e944a964495be11b57163269a870d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:UTHEUF2KPEAJXJGYAH52J5KS4Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integrability of graph combinatorics via random walks and heaps of dimers","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"E. Guitter, P. Di Francesco","submitted_at":"2005-06-27T14:37:29Z","abstract_excerpt":"We investigate the integrability of the discrete non-linear equation governing the dependence on geodesic distance of planar graphs with inner vertices of even valences. This equation follows from a bijection between graphs and blossom trees and is expressed in terms of generating functions for random walks. We construct explicitly an infinite set of conserved quantities for this equation, also involving suitable combinations of random walk generating functions. The proof of their conservation, i.e. their eventual independence on the geodesic distance, relies on the connection between random w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506542","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":"2026-05-18T01:05:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U+IPMnMuvtSuOAnW5xq5KDd4X4bF7LoiNA+gsjLK+JIoPe1EvQMML5Up5mPoKJi7id5meMtzDDGdvQx+q41gDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:08:23.452302Z"},"content_sha256":"15b1e27f1d8bf6a4c41c0f73a14e060788ad11baf5e0f620a5afb90de0e2a103","schema_version":"1.0","event_id":"sha256:15b1e27f1d8bf6a4c41c0f73a14e060788ad11baf5e0f620a5afb90de0e2a103"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UTHEUF2KPEAJXJGYAH52J5KS4Y/bundle.json","state_url":"https://pith.science/pith/UTHEUF2KPEAJXJGYAH52J5KS4Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UTHEUF2KPEAJXJGYAH52J5KS4Y/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":"2026-06-03T05:08:23Z","links":{"resolver":"https://pith.science/pith/UTHEUF2KPEAJXJGYAH52J5KS4Y","bundle":"https://pith.science/pith/UTHEUF2KPEAJXJGYAH52J5KS4Y/bundle.json","state":"https://pith.science/pith/UTHEUF2KPEAJXJGYAH52J5KS4Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UTHEUF2KPEAJXJGYAH52J5KS4Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:UTHEUF2KPEAJXJGYAH52J5KS4Y","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":"2c190a4dd86977088e3d9e0b25b2eada0956cc1fa20ed9bffa3809191ce76f84","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.CO","submitted_at":"2005-06-27T14:37:29Z","title_canon_sha256":"9974f2715199c1074d272a80da5cfc6e1dd8611b5fa19e1bf860f0a3102f8799"},"schema_version":"1.0","source":{"id":"math/0506542","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0506542","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0506542v1","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506542","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"UTHEUF2KPEAJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"UTHEUF2KPEAJXJGY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"UTHEUF2K","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:15b1e27f1d8bf6a4c41c0f73a14e060788ad11baf5e0f620a5afb90de0e2a103","target":"graph","created_at":"2026-05-18T01:05:23Z","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":"We investigate the integrability of the discrete non-linear equation governing the dependence on geodesic distance of planar graphs with inner vertices of even valences. This equation follows from a bijection between graphs and blossom trees and is expressed in terms of generating functions for random walks. We construct explicitly an infinite set of conserved quantities for this equation, also involving suitable combinations of random walk generating functions. The proof of their conservation, i.e. their eventual independence on the geodesic distance, relies on the connection between random w","authors_text":"E. Guitter, P. Di Francesco","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2005-06-27T14:37:29Z","title":"Integrability of graph combinatorics via random walks and heaps of dimers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506542","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:ba1ac69368d75925a04a2fc23efeb865d63e944a964495be11b57163269a870d","target":"record","created_at":"2026-05-18T01:05:23Z","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":"2c190a4dd86977088e3d9e0b25b2eada0956cc1fa20ed9bffa3809191ce76f84","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.CO","submitted_at":"2005-06-27T14:37:29Z","title_canon_sha256":"9974f2715199c1074d272a80da5cfc6e1dd8611b5fa19e1bf860f0a3102f8799"},"schema_version":"1.0","source":{"id":"math/0506542","kind":"arxiv","version":1}},"canonical_sha256":"a4ce4a174a79009ba4d801fba4f552e614cb10937b5ad113b5611e12b2a456f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4ce4a174a79009ba4d801fba4f552e614cb10937b5ad113b5611e12b2a456f4","first_computed_at":"2026-05-18T01:05:23.364745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:23.364745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WReBBM4K0r7cS6dIWg69RUA5iDQUXJMwterf9MPFDhf415obRaRk8nexi34asTIfSPUGKiQ9FCdIGT6ZpPHZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:23.365245Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0506542","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba1ac69368d75925a04a2fc23efeb865d63e944a964495be11b57163269a870d","sha256:15b1e27f1d8bf6a4c41c0f73a14e060788ad11baf5e0f620a5afb90de0e2a103"],"state_sha256":"d0e9590849bd8a51dd05f8928ab28d220f6a204dd8e4abfbf92d00e4200b2a18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6cxZohcZxhhi1toy6I4czuaMkWHZI+7M2SWpqxLZ9N3e32E1RWx2AZSyvXlut4vuEAMX/1p32GHLSxsBwJvsDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:08:23.454326Z","bundle_sha256":"e065fd992d7a988fed186880d3b5f9aaf397a1d63f19fa9ea22bd4a3c652eb44"}}