{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GFZJ6L2VPP3F6SH65R7ZC2HPHH","short_pith_number":"pith:GFZJ6L2V","canonical_record":{"source":{"id":"1102.5308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-25T18:41:10Z","cross_cats_sorted":[],"title_canon_sha256":"a9341a0ed95ff376c4189017ffc4cf0874af6e93bf94b325476eda1f567ee171","abstract_canon_sha256":"f511b7f45d4a6b6dc48ea26a475eb5fc22c2c1303ceff53b2e4fbdf59d7bed51"},"schema_version":"1.0"},"canonical_sha256":"31729f2f557bf65f48feec7f9168ef39d7634a80c5b94f649c6643fdd1c21b66","source":{"kind":"arxiv","id":"1102.5308","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5308","created_at":"2026-05-18T00:19:49Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5308v1","created_at":"2026-05-18T00:19:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5308","created_at":"2026-05-18T00:19:49Z"},{"alias_kind":"pith_short_12","alias_value":"GFZJ6L2VPP3F","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GFZJ6L2VPP3F6SH6","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GFZJ6L2V","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GFZJ6L2VPP3F6SH65R7ZC2HPHH","target":"record","payload":{"canonical_record":{"source":{"id":"1102.5308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-25T18:41:10Z","cross_cats_sorted":[],"title_canon_sha256":"a9341a0ed95ff376c4189017ffc4cf0874af6e93bf94b325476eda1f567ee171","abstract_canon_sha256":"f511b7f45d4a6b6dc48ea26a475eb5fc22c2c1303ceff53b2e4fbdf59d7bed51"},"schema_version":"1.0"},"canonical_sha256":"31729f2f557bf65f48feec7f9168ef39d7634a80c5b94f649c6643fdd1c21b66","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:49.374670Z","signature_b64":"WApYd+nMg75nOjAnpHAaU6APJ9cW/vcyAFgla0Ncr+Xb6j3EuZ/bvMXMDRelhEZXmgoRRdXALDPuYYYmeWDaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31729f2f557bf65f48feec7f9168ef39d7634a80c5b94f649c6643fdd1c21b66","last_reissued_at":"2026-05-18T00:19:49.373935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:49.373935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.5308","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":"2026-05-18T00:19:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mgGnP4iSjz6PC6X5XS6grXAgKZ8783/lRzYLLG/ebbkBNk4qjssOJtRkMluDYO0/qzYPL71/IBDSjbHnnmGsDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T21:16:01.316430Z"},"content_sha256":"d34d71951f03d4e150175b57b9ffdbcaa86d82f8e7933418b0bd13a64ef3b4aa","schema_version":"1.0","event_id":"sha256:d34d71951f03d4e150175b57b9ffdbcaa86d82f8e7933418b0bd13a64ef3b4aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GFZJ6L2VPP3F6SH65R7ZC2HPHH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A refinement of the A-polynomial of quivers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Fernando Rodriguez Villegas","submitted_at":"2011-02-25T18:41:10Z","abstract_excerpt":"We study a refinement of the A-polynomial in the case of the g-loop quiver. We give an explicit formula for its value at q=1. Conjecturally this implies a formula for the middle Betti number of the moduli space of Higgs bundles or equivalently of the character variety of a Riemann surface of genus g."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5308","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":"2026-05-18T00:19:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6F8mCBgUomTgjrPCwY4P3Dj8s4wWxZmEXHWHfWIbrLzJCIPtCbsRosLnlBVU4jR2wvVMNFs5eJ7FNFSr6JpxAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T21:16:01.316899Z"},"content_sha256":"58bdb1a4c80a9439143ecd070e62d3ff801fffd72473a33aff40f8866fce6db6","schema_version":"1.0","event_id":"sha256:58bdb1a4c80a9439143ecd070e62d3ff801fffd72473a33aff40f8866fce6db6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GFZJ6L2VPP3F6SH65R7ZC2HPHH/bundle.json","state_url":"https://pith.science/pith/GFZJ6L2VPP3F6SH65R7ZC2HPHH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GFZJ6L2VPP3F6SH65R7ZC2HPHH/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":"2026-08-13T21:16:01Z","links":{"resolver":"https://pith.science/pith/GFZJ6L2VPP3F6SH65R7ZC2HPHH","bundle":"https://pith.science/pith/GFZJ6L2VPP3F6SH65R7ZC2HPHH/bundle.json","state":"https://pith.science/pith/GFZJ6L2VPP3F6SH65R7ZC2HPHH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GFZJ6L2VPP3F6SH65R7ZC2HPHH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GFZJ6L2VPP3F6SH65R7ZC2HPHH","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":"f511b7f45d4a6b6dc48ea26a475eb5fc22c2c1303ceff53b2e4fbdf59d7bed51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-25T18:41:10Z","title_canon_sha256":"a9341a0ed95ff376c4189017ffc4cf0874af6e93bf94b325476eda1f567ee171"},"schema_version":"1.0","source":{"id":"1102.5308","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5308","created_at":"2026-05-18T00:19:49Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5308v1","created_at":"2026-05-18T00:19:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5308","created_at":"2026-05-18T00:19:49Z"},{"alias_kind":"pith_short_12","alias_value":"GFZJ6L2VPP3F","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GFZJ6L2VPP3F6SH6","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GFZJ6L2V","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:58bdb1a4c80a9439143ecd070e62d3ff801fffd72473a33aff40f8866fce6db6","target":"graph","created_at":"2026-05-18T00:19:49Z","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 study a refinement of the A-polynomial in the case of the g-loop quiver. We give an explicit formula for its value at q=1. Conjecturally this implies a formula for the middle Betti number of the moduli space of Higgs bundles or equivalently of the character variety of a Riemann surface of genus g.","authors_text":"Fernando Rodriguez Villegas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-25T18:41:10Z","title":"A refinement of the A-polynomial of quivers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5308","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:d34d71951f03d4e150175b57b9ffdbcaa86d82f8e7933418b0bd13a64ef3b4aa","target":"record","created_at":"2026-05-18T00:19:49Z","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":"f511b7f45d4a6b6dc48ea26a475eb5fc22c2c1303ceff53b2e4fbdf59d7bed51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-25T18:41:10Z","title_canon_sha256":"a9341a0ed95ff376c4189017ffc4cf0874af6e93bf94b325476eda1f567ee171"},"schema_version":"1.0","source":{"id":"1102.5308","kind":"arxiv","version":1}},"canonical_sha256":"31729f2f557bf65f48feec7f9168ef39d7634a80c5b94f649c6643fdd1c21b66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31729f2f557bf65f48feec7f9168ef39d7634a80c5b94f649c6643fdd1c21b66","first_computed_at":"2026-05-18T00:19:49.373935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:49.373935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WApYd+nMg75nOjAnpHAaU6APJ9cW/vcyAFgla0Ncr+Xb6j3EuZ/bvMXMDRelhEZXmgoRRdXALDPuYYYmeWDaDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:49.374670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.5308","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d34d71951f03d4e150175b57b9ffdbcaa86d82f8e7933418b0bd13a64ef3b4aa","sha256:58bdb1a4c80a9439143ecd070e62d3ff801fffd72473a33aff40f8866fce6db6"],"state_sha256":"48b533b641e5e97da95e89b1134832d7c64ffe5c7c8b4083ccf69b970668fbdf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UWhr0sEDsfq+fIbOIaAwDOtQpxGF2gDSyux9Ada8FNcuyHvpOCTZwxT0kF8Tr7bE+zrW/ZGYkFXR9iat1aJQCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T21:16:01.358488Z","bundle_sha256":"64d2e076dd5406068155b82f8d3bacca7380df145b2718e781acedcfd93330fc"}}