{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:UV2PDBRCEQX5XHZEWAE6VMC3TQ","short_pith_number":"pith:UV2PDBRC","canonical_record":{"source":{"id":"2501.15483","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-01-26T11:04:49Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5c7beb8c2d1a8b09952993049b2d9549bd33e5773ffe64cc9750994240dd3036","abstract_canon_sha256":"191051eeddeae44397ec23383f653582c169b86bfa976b6fcd0d00ccd611a680"},"schema_version":"1.0"},"canonical_sha256":"a574f18622242fdb9f24b009eab05b9c1075f96e628d95d63b19197b7b88428f","source":{"kind":"arxiv","id":"2501.15483","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.15483","created_at":"2026-07-05T10:25:16Z"},{"alias_kind":"arxiv_version","alias_value":"2501.15483v4","created_at":"2026-07-05T10:25:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.15483","created_at":"2026-07-05T10:25:16Z"},{"alias_kind":"pith_short_12","alias_value":"UV2PDBRCEQX5","created_at":"2026-07-05T10:25:16Z"},{"alias_kind":"pith_short_16","alias_value":"UV2PDBRCEQX5XHZE","created_at":"2026-07-05T10:25:16Z"},{"alias_kind":"pith_short_8","alias_value":"UV2PDBRC","created_at":"2026-07-05T10:25:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:UV2PDBRCEQX5XHZEWAE6VMC3TQ","target":"record","payload":{"canonical_record":{"source":{"id":"2501.15483","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-01-26T11:04:49Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5c7beb8c2d1a8b09952993049b2d9549bd33e5773ffe64cc9750994240dd3036","abstract_canon_sha256":"191051eeddeae44397ec23383f653582c169b86bfa976b6fcd0d00ccd611a680"},"schema_version":"1.0"},"canonical_sha256":"a574f18622242fdb9f24b009eab05b9c1075f96e628d95d63b19197b7b88428f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:25:16.394365Z","signature_b64":"7ciHvRQzUmM62J1rnntglRTPWNsqaJbsCB+68xi0oeSdlteaj4i0nCtdxIMjmp2UT1ZZ/e4yi6bg7Ucsy0jjDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a574f18622242fdb9f24b009eab05b9c1075f96e628d95d63b19197b7b88428f","last_reissued_at":"2026-07-05T10:25:16.393836Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:25:16.393836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.15483","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:25:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XU8I9L4imqkKxSEqUzpLjMGFo0hbTKMuTHBS0IarJL7+z2OonrTHrXCxKGYKnk/hk/TMfU3lErZUbiG39/tFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T19:44:24.139618Z"},"content_sha256":"1a3dcf36b7fef7c36b1bd7a53f7123c316d43e6ed6408a5fbc479a901c27bd76","schema_version":"1.0","event_id":"sha256:1a3dcf36b7fef7c36b1bd7a53f7123c316d43e6ed6408a5fbc479a901c27bd76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:UV2PDBRCEQX5XHZEWAE6VMC3TQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Integrable Snake Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Rohan Shiatis, Samuel G. G. Johnston","submitted_at":"2025-01-26T11:04:49Z","abstract_excerpt":"A pure snake configuration is a bijection $\\sigma:\\mathbb{Z}^2 \\to \\mathbb{Z}^2$ containing no two-cycles and such that for each $x \\in \\mathbb{Z}^2$ we have $\\sigma(x) \\in \\{ x , x+ \\mathbf{e}^1, x+\\mathbf{e}^2 , x- \\mathbf{e}^2 \\}.$ The non-trivial cycles of a pure snake configuration may be regarded as a collection of non-intersecting paths in $\\mathbb{Z}^2$ that may travel right, up, or down (but not left) from a given vertex. Pure snake configurations are a generalisation of lozenge tilings, which are in natural correspondence with paths that only travel right or up. We introduce a partit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.15483","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.15483/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:25:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GCt5i+Hf8A7eE+ydsl3EYeq2YYDHTX7oWpNFwX0MS1fa9mZ8PkxzHkkgIrAkmWchcsXD+U8880+a0FYklgv4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T19:44:24.140137Z"},"content_sha256":"d4b705c10d3b9ce330b3df117dbb7403f5e8f399d4e7bc30314669c480eaf936","schema_version":"1.0","event_id":"sha256:d4b705c10d3b9ce330b3df117dbb7403f5e8f399d4e7bc30314669c480eaf936"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UV2PDBRCEQX5XHZEWAE6VMC3TQ/bundle.json","state_url":"https://pith.science/pith/UV2PDBRCEQX5XHZEWAE6VMC3TQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UV2PDBRCEQX5XHZEWAE6VMC3TQ/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":"2026-08-21T19:44:24Z","links":{"resolver":"https://pith.science/pith/UV2PDBRCEQX5XHZEWAE6VMC3TQ","bundle":"https://pith.science/pith/UV2PDBRCEQX5XHZEWAE6VMC3TQ/bundle.json","state":"https://pith.science/pith/UV2PDBRCEQX5XHZEWAE6VMC3TQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UV2PDBRCEQX5XHZEWAE6VMC3TQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UV2PDBRCEQX5XHZEWAE6VMC3TQ","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":"191051eeddeae44397ec23383f653582c169b86bfa976b6fcd0d00ccd611a680","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-01-26T11:04:49Z","title_canon_sha256":"5c7beb8c2d1a8b09952993049b2d9549bd33e5773ffe64cc9750994240dd3036"},"schema_version":"1.0","source":{"id":"2501.15483","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.15483","created_at":"2026-07-05T10:25:16Z"},{"alias_kind":"arxiv_version","alias_value":"2501.15483v4","created_at":"2026-07-05T10:25:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.15483","created_at":"2026-07-05T10:25:16Z"},{"alias_kind":"pith_short_12","alias_value":"UV2PDBRCEQX5","created_at":"2026-07-05T10:25:16Z"},{"alias_kind":"pith_short_16","alias_value":"UV2PDBRCEQX5XHZE","created_at":"2026-07-05T10:25:16Z"},{"alias_kind":"pith_short_8","alias_value":"UV2PDBRC","created_at":"2026-07-05T10:25:16Z"}],"graph_snapshots":[{"event_id":"sha256:d4b705c10d3b9ce330b3df117dbb7403f5e8f399d4e7bc30314669c480eaf936","target":"graph","created_at":"2026-07-05T10:25:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.15483/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A pure snake configuration is a bijection $\\sigma:\\mathbb{Z}^2 \\to \\mathbb{Z}^2$ containing no two-cycles and such that for each $x \\in \\mathbb{Z}^2$ we have $\\sigma(x) \\in \\{ x , x+ \\mathbf{e}^1, x+\\mathbf{e}^2 , x- \\mathbf{e}^2 \\}.$ The non-trivial cycles of a pure snake configuration may be regarded as a collection of non-intersecting paths in $\\mathbb{Z}^2$ that may travel right, up, or down (but not left) from a given vertex. Pure snake configurations are a generalisation of lozenge tilings, which are in natural correspondence with paths that only travel right or up. We introduce a partit","authors_text":"Rohan Shiatis, Samuel G. G. Johnston","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-01-26T11:04:49Z","title":"The Integrable Snake Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.15483","kind":"arxiv","version":4},"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":"sha256:1a3dcf36b7fef7c36b1bd7a53f7123c316d43e6ed6408a5fbc479a901c27bd76","target":"record","created_at":"2026-07-05T10:25:16Z","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":"191051eeddeae44397ec23383f653582c169b86bfa976b6fcd0d00ccd611a680","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-01-26T11:04:49Z","title_canon_sha256":"5c7beb8c2d1a8b09952993049b2d9549bd33e5773ffe64cc9750994240dd3036"},"schema_version":"1.0","source":{"id":"2501.15483","kind":"arxiv","version":4}},"canonical_sha256":"a574f18622242fdb9f24b009eab05b9c1075f96e628d95d63b19197b7b88428f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a574f18622242fdb9f24b009eab05b9c1075f96e628d95d63b19197b7b88428f","first_computed_at":"2026-07-05T10:25:16.393836Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:25:16.393836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ciHvRQzUmM62J1rnntglRTPWNsqaJbsCB+68xi0oeSdlteaj4i0nCtdxIMjmp2UT1ZZ/e4yi6bg7Ucsy0jjDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:25:16.394365Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.15483","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a3dcf36b7fef7c36b1bd7a53f7123c316d43e6ed6408a5fbc479a901c27bd76","sha256:d4b705c10d3b9ce330b3df117dbb7403f5e8f399d4e7bc30314669c480eaf936"],"state_sha256":"2d56bf1a954e9b2ad4dce83c898bcc00c1287ed96cdd5bc11d6886082f280281"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d90fN5RrS359Fm1NR2Svp7hs2hzAdVuOW0HclEpu/jEChRwPHoIDeGb6oI75fJ/8YszczWbiNjRM3e5XeUvTDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T19:44:24.144074Z","bundle_sha256":"e61c442cc1ced8d87861bcf5c76aca2fe5edd3632113e2fe25e7ce5c46becb4a"}}