{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:KIT3FXRDRDVUBIUQN6LH3GS4T2","short_pith_number":"pith:KIT3FXRD","canonical_record":{"source":{"id":"2411.11676","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-11-18T15:56:37Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"5840f543c6c00d24a683d19102b2c669bf87a8401ee35fe528599b8b9ae9129e","abstract_canon_sha256":"5c3c846ac311cdd61137a11fbc95cdb67bab3e58687be5c7593d4341c745a2d6"},"schema_version":"1.0"},"canonical_sha256":"5227b2de2388eb40a2906f967d9a5c9e97428158b9ebcff24b20ac3d546b9b4f","source":{"kind":"arxiv","id":"2411.11676","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.11676","created_at":"2026-07-05T11:56:16Z"},{"alias_kind":"arxiv_version","alias_value":"2411.11676v2","created_at":"2026-07-05T11:56:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.11676","created_at":"2026-07-05T11:56:16Z"},{"alias_kind":"pith_short_12","alias_value":"KIT3FXRDRDVU","created_at":"2026-07-05T11:56:16Z"},{"alias_kind":"pith_short_16","alias_value":"KIT3FXRDRDVUBIUQ","created_at":"2026-07-05T11:56:16Z"},{"alias_kind":"pith_short_8","alias_value":"KIT3FXRD","created_at":"2026-07-05T11:56:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:KIT3FXRDRDVUBIUQN6LH3GS4T2","target":"record","payload":{"canonical_record":{"source":{"id":"2411.11676","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-11-18T15:56:37Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"5840f543c6c00d24a683d19102b2c669bf87a8401ee35fe528599b8b9ae9129e","abstract_canon_sha256":"5c3c846ac311cdd61137a11fbc95cdb67bab3e58687be5c7593d4341c745a2d6"},"schema_version":"1.0"},"canonical_sha256":"5227b2de2388eb40a2906f967d9a5c9e97428158b9ebcff24b20ac3d546b9b4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:56:16.220266Z","signature_b64":"VEFj5yj2jAeDX9terhU5a5tkVqkaArR1dmXDOIi5Ad8znN2IEtY2ADOJxTJD9E/tuq1P8YNCoh8G7ulfaF+pCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5227b2de2388eb40a2906f967d9a5c9e97428158b9ebcff24b20ac3d546b9b4f","last_reissued_at":"2026-07-05T11:56:16.219831Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:56:16.219831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.11676","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:56:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VOeVQ2fNZKKj0kbZIQvFXEYLY+tW2wsRaYQFrjm83YYKHE5GS5bhTLzXx3nXafNax4o3bzTgXG47nqrjVwjvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T01:06:47.364954Z"},"content_sha256":"632613f625e227fc36fba18eaa0e0403efbed6a1d5295a1eb04f84250a99c679","schema_version":"1.0","event_id":"sha256:632613f625e227fc36fba18eaa0e0403efbed6a1d5295a1eb04f84250a99c679"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:KIT3FXRDRDVUBIUQN6LH3GS4T2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Surface sums for lattice Yang-Mills in the large-$N$ limit","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.PR","authors_text":"Jacopo Borga, Jasper Shogren-Knaak, Sky Cao","submitted_at":"2024-11-18T15:56:37Z","abstract_excerpt":"We give a sum over weighted planar surfaces formula for Wilson loop expectations in the large-$N$ limit of strongly coupled lattice Yang-Mills theory, in any dimension. The weights of each surface are simple and expressed in terms of products of signed Catalan numbers.\n  In establishing our results, the main novelty is to convert a recursive relation for Wilson loop expectations, known as the master loop equation, into a new peeling exploration of the planar surfaces. This exploration reveals hidden cancellations within the sums, enabling a deeper understanding of the structure of the planar s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.11676","kind":"arxiv","version":2},"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/2411.11676/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":"2026-07-05T11:56:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LDsV6OmIG0OMiZLfeSp3Li2RYNrx5QWWpZe4pL1pR//QJ2rY/m5/iUnG17VGdAYgFsEDcbi4mx4GijUBtvKABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T01:06:47.365354Z"},"content_sha256":"08110451b7850bd512c239236035581a3cf1e90952032f9d1597ad1c77f4888c","schema_version":"1.0","event_id":"sha256:08110451b7850bd512c239236035581a3cf1e90952032f9d1597ad1c77f4888c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KIT3FXRDRDVUBIUQN6LH3GS4T2/bundle.json","state_url":"https://pith.science/pith/KIT3FXRDRDVUBIUQN6LH3GS4T2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KIT3FXRDRDVUBIUQN6LH3GS4T2/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":"2026-08-11T01:06:47Z","links":{"resolver":"https://pith.science/pith/KIT3FXRDRDVUBIUQN6LH3GS4T2","bundle":"https://pith.science/pith/KIT3FXRDRDVUBIUQN6LH3GS4T2/bundle.json","state":"https://pith.science/pith/KIT3FXRDRDVUBIUQN6LH3GS4T2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KIT3FXRDRDVUBIUQN6LH3GS4T2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KIT3FXRDRDVUBIUQN6LH3GS4T2","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":"5c3c846ac311cdd61137a11fbc95cdb67bab3e58687be5c7593d4341c745a2d6","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-11-18T15:56:37Z","title_canon_sha256":"5840f543c6c00d24a683d19102b2c669bf87a8401ee35fe528599b8b9ae9129e"},"schema_version":"1.0","source":{"id":"2411.11676","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.11676","created_at":"2026-07-05T11:56:16Z"},{"alias_kind":"arxiv_version","alias_value":"2411.11676v2","created_at":"2026-07-05T11:56:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.11676","created_at":"2026-07-05T11:56:16Z"},{"alias_kind":"pith_short_12","alias_value":"KIT3FXRDRDVU","created_at":"2026-07-05T11:56:16Z"},{"alias_kind":"pith_short_16","alias_value":"KIT3FXRDRDVUBIUQ","created_at":"2026-07-05T11:56:16Z"},{"alias_kind":"pith_short_8","alias_value":"KIT3FXRD","created_at":"2026-07-05T11:56:16Z"}],"graph_snapshots":[{"event_id":"sha256:08110451b7850bd512c239236035581a3cf1e90952032f9d1597ad1c77f4888c","target":"graph","created_at":"2026-07-05T11:56:16Z","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/2411.11676/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a sum over weighted planar surfaces formula for Wilson loop expectations in the large-$N$ limit of strongly coupled lattice Yang-Mills theory, in any dimension. The weights of each surface are simple and expressed in terms of products of signed Catalan numbers.\n  In establishing our results, the main novelty is to convert a recursive relation for Wilson loop expectations, known as the master loop equation, into a new peeling exploration of the planar surfaces. This exploration reveals hidden cancellations within the sums, enabling a deeper understanding of the structure of the planar s","authors_text":"Jacopo Borga, Jasper Shogren-Knaak, Sky Cao","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-11-18T15:56:37Z","title":"Surface sums for lattice Yang-Mills in the large-$N$ limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.11676","kind":"arxiv","version":2},"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":"sha256:632613f625e227fc36fba18eaa0e0403efbed6a1d5295a1eb04f84250a99c679","target":"record","created_at":"2026-07-05T11:56:16Z","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":"5c3c846ac311cdd61137a11fbc95cdb67bab3e58687be5c7593d4341c745a2d6","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-11-18T15:56:37Z","title_canon_sha256":"5840f543c6c00d24a683d19102b2c669bf87a8401ee35fe528599b8b9ae9129e"},"schema_version":"1.0","source":{"id":"2411.11676","kind":"arxiv","version":2}},"canonical_sha256":"5227b2de2388eb40a2906f967d9a5c9e97428158b9ebcff24b20ac3d546b9b4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5227b2de2388eb40a2906f967d9a5c9e97428158b9ebcff24b20ac3d546b9b4f","first_computed_at":"2026-07-05T11:56:16.219831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:56:16.219831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VEFj5yj2jAeDX9terhU5a5tkVqkaArR1dmXDOIi5Ad8znN2IEtY2ADOJxTJD9E/tuq1P8YNCoh8G7ulfaF+pCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:56:16.220266Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.11676","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:632613f625e227fc36fba18eaa0e0403efbed6a1d5295a1eb04f84250a99c679","sha256:08110451b7850bd512c239236035581a3cf1e90952032f9d1597ad1c77f4888c"],"state_sha256":"f909655528fdc016c69fcbdf1b3cdfbf1fb4d65bbb9952f07df0c7be31ef3822"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g/TngVDWD0IfnOu4atCqVyaq5xUYq+hK/p+YDXe6I8QlGbyQXdHUponxzRrfKX85N1/JbhDD6n9mxt56nfHFCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T01:06:47.369291Z","bundle_sha256":"574ace8fd302dc9cd780da5951b9f1ee98657977a8f33ac2d5d9715f18598966"}}