{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:OVBPZS57BEO3JZOUDRLEXC63JU","short_pith_number":"pith:OVBPZS57","canonical_record":{"source":{"id":"2105.01543","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2021-05-04T14:54:09Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"06987f9705deaa01ae0fda7cb4c1a0cd8dc767ab670bbeb7015d5a9cabf7b53e","abstract_canon_sha256":"c18c8ae12f92e9b25ca3de3ee1b08304a170175d88bc5efe0f75a21850972aee"},"schema_version":"1.0"},"canonical_sha256":"7542fccbbf091db4e5d41c564b8bdb4d196094b02d6861c3e7202682997a9991","source":{"kind":"arxiv","id":"2105.01543","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.01543","created_at":"2026-07-05T02:41:20Z"},{"alias_kind":"arxiv_version","alias_value":"2105.01543v1","created_at":"2026-07-05T02:41:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.01543","created_at":"2026-07-05T02:41:20Z"},{"alias_kind":"pith_short_12","alias_value":"OVBPZS57BEO3","created_at":"2026-07-05T02:41:20Z"},{"alias_kind":"pith_short_16","alias_value":"OVBPZS57BEO3JZOU","created_at":"2026-07-05T02:41:20Z"},{"alias_kind":"pith_short_8","alias_value":"OVBPZS57","created_at":"2026-07-05T02:41:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:OVBPZS57BEO3JZOUDRLEXC63JU","target":"record","payload":{"canonical_record":{"source":{"id":"2105.01543","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2021-05-04T14:54:09Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"06987f9705deaa01ae0fda7cb4c1a0cd8dc767ab670bbeb7015d5a9cabf7b53e","abstract_canon_sha256":"c18c8ae12f92e9b25ca3de3ee1b08304a170175d88bc5efe0f75a21850972aee"},"schema_version":"1.0"},"canonical_sha256":"7542fccbbf091db4e5d41c564b8bdb4d196094b02d6861c3e7202682997a9991","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:41:20.854512Z","signature_b64":"fvlUMIsDfmuvG4iREIyO6GtyOOYCt9opXZbS4cllXAUrCV7OTx3h+Ac6uv7QAAhORgti7qc/9+YAQxEO1tXqBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7542fccbbf091db4e5d41c564b8bdb4d196094b02d6861c3e7202682997a9991","last_reissued_at":"2026-07-05T02:41:20.854079Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:41:20.854079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.01543","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":"2026-07-05T02:41:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aNL6jkOQEkvU6/As2USaff1eIhkRWii/QDkDVaZqSHkz3zcyrhPHLfei9PCH9dMfOhSxXFAFMt5ulRvC96gVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T01:10:29.055385Z"},"content_sha256":"0999c5c7055fc8be354f0db4b8a7aaabecca31ff6452dd3810ae9b3255e18594","schema_version":"1.0","event_id":"sha256:0999c5c7055fc8be354f0db4b8a7aaabecca31ff6452dd3810ae9b3255e18594"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:OVBPZS57BEO3JZOUDRLEXC63JU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On webs, polylogarithms and cluster algebras","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Luc Pirio","submitted_at":"2021-05-04T14:54:09Z","abstract_excerpt":"In this text, we investigate webs which can be associated to cluster algebras from the point of view of the abelian functional equations these webs carry, focusing on the polylogarithmic ones. We introduce a general notion of webs whose rank is `As Maximal as Possible' (AMP) and show that many webs associated either to polylogarithmic functional equations or to cluster algebras are of this type. In particular, we prove a few results and state some conjectures about cluster webs associated to (pairs of) Dynkin diagrams. Along the way, we show that many of the classical functional equations sati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.01543","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.01543/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":"2026-07-05T02:41:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gqvkKyJp9xxPGJguwmixrh+A35aL4D2Z5I5uyzD6ogox3dRdGpsb9a7G/Sm3CFDWBWD9wyR7vMAo/D54YSOiCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T01:10:29.055923Z"},"content_sha256":"606e99daeecfbb265430ca41fbaa0831bd7b45d9ac284af1143758ca43ff49c3","schema_version":"1.0","event_id":"sha256:606e99daeecfbb265430ca41fbaa0831bd7b45d9ac284af1143758ca43ff49c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OVBPZS57BEO3JZOUDRLEXC63JU/bundle.json","state_url":"https://pith.science/pith/OVBPZS57BEO3JZOUDRLEXC63JU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OVBPZS57BEO3JZOUDRLEXC63JU/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":"2026-08-08T01:10:29Z","links":{"resolver":"https://pith.science/pith/OVBPZS57BEO3JZOUDRLEXC63JU","bundle":"https://pith.science/pith/OVBPZS57BEO3JZOUDRLEXC63JU/bundle.json","state":"https://pith.science/pith/OVBPZS57BEO3JZOUDRLEXC63JU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OVBPZS57BEO3JZOUDRLEXC63JU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:OVBPZS57BEO3JZOUDRLEXC63JU","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":"c18c8ae12f92e9b25ca3de3ee1b08304a170175d88bc5efe0f75a21850972aee","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2021-05-04T14:54:09Z","title_canon_sha256":"06987f9705deaa01ae0fda7cb4c1a0cd8dc767ab670bbeb7015d5a9cabf7b53e"},"schema_version":"1.0","source":{"id":"2105.01543","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.01543","created_at":"2026-07-05T02:41:20Z"},{"alias_kind":"arxiv_version","alias_value":"2105.01543v1","created_at":"2026-07-05T02:41:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.01543","created_at":"2026-07-05T02:41:20Z"},{"alias_kind":"pith_short_12","alias_value":"OVBPZS57BEO3","created_at":"2026-07-05T02:41:20Z"},{"alias_kind":"pith_short_16","alias_value":"OVBPZS57BEO3JZOU","created_at":"2026-07-05T02:41:20Z"},{"alias_kind":"pith_short_8","alias_value":"OVBPZS57","created_at":"2026-07-05T02:41:20Z"}],"graph_snapshots":[{"event_id":"sha256:606e99daeecfbb265430ca41fbaa0831bd7b45d9ac284af1143758ca43ff49c3","target":"graph","created_at":"2026-07-05T02:41:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2105.01543/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this text, we investigate webs which can be associated to cluster algebras from the point of view of the abelian functional equations these webs carry, focusing on the polylogarithmic ones. We introduce a general notion of webs whose rank is `As Maximal as Possible' (AMP) and show that many webs associated either to polylogarithmic functional equations or to cluster algebras are of this type. In particular, we prove a few results and state some conjectures about cluster webs associated to (pairs of) Dynkin diagrams. Along the way, we show that many of the classical functional equations sati","authors_text":"Luc Pirio","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2021-05-04T14:54:09Z","title":"On webs, polylogarithms and cluster algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.01543","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":"sha256:0999c5c7055fc8be354f0db4b8a7aaabecca31ff6452dd3810ae9b3255e18594","target":"record","created_at":"2026-07-05T02:41:20Z","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":"c18c8ae12f92e9b25ca3de3ee1b08304a170175d88bc5efe0f75a21850972aee","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2021-05-04T14:54:09Z","title_canon_sha256":"06987f9705deaa01ae0fda7cb4c1a0cd8dc767ab670bbeb7015d5a9cabf7b53e"},"schema_version":"1.0","source":{"id":"2105.01543","kind":"arxiv","version":1}},"canonical_sha256":"7542fccbbf091db4e5d41c564b8bdb4d196094b02d6861c3e7202682997a9991","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7542fccbbf091db4e5d41c564b8bdb4d196094b02d6861c3e7202682997a9991","first_computed_at":"2026-07-05T02:41:20.854079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:41:20.854079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fvlUMIsDfmuvG4iREIyO6GtyOOYCt9opXZbS4cllXAUrCV7OTx3h+Ac6uv7QAAhORgti7qc/9+YAQxEO1tXqBg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:41:20.854512Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.01543","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0999c5c7055fc8be354f0db4b8a7aaabecca31ff6452dd3810ae9b3255e18594","sha256:606e99daeecfbb265430ca41fbaa0831bd7b45d9ac284af1143758ca43ff49c3"],"state_sha256":"353c4810d6970969d473dfcf2729642fd874be9cc4ec24dc51b12a1c69b0a94b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eE+owclCWLGXGrrP83rzej/8tnlm0g2Q48DCIIo7ivReovspFiHfbI8HPPEgwaMUNgddaIron9CUrxKqAuDOCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T01:10:29.061623Z","bundle_sha256":"0f7ce049d3251810647e24a20d2b55585ca17e169729493b3e31547640a30b0b"}}