{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:TUG6YSS4XTLW22WOQUYL3IBLMS","short_pith_number":"pith:TUG6YSS4","canonical_record":{"source":{"id":"2503.16370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-03-20T17:28:38Z","cross_cats_sorted":["math.AG","math.DG"],"title_canon_sha256":"6f5556890b99608e3c6b306637aeb85e1f23d44e0bc17eb8ef2b049ebdf2144a","abstract_canon_sha256":"2db0a4c7c364727e8a310c430cfdbc6620e5f5c2329b41f29002e54ea80bd6df"},"schema_version":"1.0"},"canonical_sha256":"9d0dec4a5cbcd76d6ace8530bda02b64aec5200e55ce097bcb9a4f4b4dd2525e","source":{"kind":"arxiv","id":"2503.16370","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.16370","created_at":"2026-07-05T10:36:18Z"},{"alias_kind":"arxiv_version","alias_value":"2503.16370v1","created_at":"2026-07-05T10:36:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.16370","created_at":"2026-07-05T10:36:18Z"},{"alias_kind":"pith_short_12","alias_value":"TUG6YSS4XTLW","created_at":"2026-07-05T10:36:18Z"},{"alias_kind":"pith_short_16","alias_value":"TUG6YSS4XTLW22WO","created_at":"2026-07-05T10:36:18Z"},{"alias_kind":"pith_short_8","alias_value":"TUG6YSS4","created_at":"2026-07-05T10:36:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:TUG6YSS4XTLW22WOQUYL3IBLMS","target":"record","payload":{"canonical_record":{"source":{"id":"2503.16370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-03-20T17:28:38Z","cross_cats_sorted":["math.AG","math.DG"],"title_canon_sha256":"6f5556890b99608e3c6b306637aeb85e1f23d44e0bc17eb8ef2b049ebdf2144a","abstract_canon_sha256":"2db0a4c7c364727e8a310c430cfdbc6620e5f5c2329b41f29002e54ea80bd6df"},"schema_version":"1.0"},"canonical_sha256":"9d0dec4a5cbcd76d6ace8530bda02b64aec5200e55ce097bcb9a4f4b4dd2525e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:36:18.217118Z","signature_b64":"eRdaONKPhxdhpsu2zma1iDNh5CLmVke60Nn1clsJUC6yLZQuNeAsz6hDa169TMwR0+4T6wp4b5sUlE3O9oNZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d0dec4a5cbcd76d6ace8530bda02b64aec5200e55ce097bcb9a4f4b4dd2525e","last_reissued_at":"2026-07-05T10:36:18.216415Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:36:18.216415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.16370","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":"2026-07-05T10:36:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hzA8jQCahH4YYvL+HOaB56XrB09eju8iGLjHs4URMcZtmId62sYN8hgyZYTe59w9IfnditmZvxdwPSkMr9QNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T01:34:46.918533Z"},"content_sha256":"36e2521f7919ba92f96cbb82afe3c8d82d9fc7f17d672b2abfabf5a0c0616042","schema_version":"1.0","event_id":"sha256:36e2521f7919ba92f96cbb82afe3c8d82d9fc7f17d672b2abfabf5a0c0616042"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:TUG6YSS4XTLW22WOQUYL3IBLMS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting $SL(2,\\mathbb{C})$ connections on Seifert-fibered spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.GT","authors_text":"Juan Mu\\~noz-Ech\\'aniz","submitted_at":"2025-03-20T17:28:38Z","abstract_excerpt":"We study the $SL(2, \\mathbb{C})$ character variety of a Seifert-fibered homology $3$-sphere from the point of view of gauge theory. Namely, we introduce a class of perturbations of the $SL(2,\\mathbb{C})$ Chern--Simons functional and prove a localisation result: the perturbed critical points either approach a compact subset of the $SL(2, \\mathbb{C})$ character variety or else `escape to infinity'. Furthermore, the Euler characteristic and Poincar\\'e polynomial of the stable locus of the character variety are obtained by suitably counting the localising critical points.\n  As an application, we o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.16370","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/2503.16370/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":"2026-07-05T10:36:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Du2ucwx3egBmK1m1LI8xIzjDUdmdutfsjvQgdcWg6XuCobwpArEXwjRaGIFuDuW97WQAjthLfaQHLhaU3yHZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T01:34:46.919028Z"},"content_sha256":"881283a367722975498d9d2b5de2923e46dd9329a8c759e6c81274cfc5d46834","schema_version":"1.0","event_id":"sha256:881283a367722975498d9d2b5de2923e46dd9329a8c759e6c81274cfc5d46834"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TUG6YSS4XTLW22WOQUYL3IBLMS/bundle.json","state_url":"https://pith.science/pith/TUG6YSS4XTLW22WOQUYL3IBLMS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TUG6YSS4XTLW22WOQUYL3IBLMS/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":"2026-08-18T01:34:46Z","links":{"resolver":"https://pith.science/pith/TUG6YSS4XTLW22WOQUYL3IBLMS","bundle":"https://pith.science/pith/TUG6YSS4XTLW22WOQUYL3IBLMS/bundle.json","state":"https://pith.science/pith/TUG6YSS4XTLW22WOQUYL3IBLMS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TUG6YSS4XTLW22WOQUYL3IBLMS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TUG6YSS4XTLW22WOQUYL3IBLMS","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":"2db0a4c7c364727e8a310c430cfdbc6620e5f5c2329b41f29002e54ea80bd6df","cross_cats_sorted":["math.AG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-03-20T17:28:38Z","title_canon_sha256":"6f5556890b99608e3c6b306637aeb85e1f23d44e0bc17eb8ef2b049ebdf2144a"},"schema_version":"1.0","source":{"id":"2503.16370","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.16370","created_at":"2026-07-05T10:36:18Z"},{"alias_kind":"arxiv_version","alias_value":"2503.16370v1","created_at":"2026-07-05T10:36:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.16370","created_at":"2026-07-05T10:36:18Z"},{"alias_kind":"pith_short_12","alias_value":"TUG6YSS4XTLW","created_at":"2026-07-05T10:36:18Z"},{"alias_kind":"pith_short_16","alias_value":"TUG6YSS4XTLW22WO","created_at":"2026-07-05T10:36:18Z"},{"alias_kind":"pith_short_8","alias_value":"TUG6YSS4","created_at":"2026-07-05T10:36:18Z"}],"graph_snapshots":[{"event_id":"sha256:881283a367722975498d9d2b5de2923e46dd9329a8c759e6c81274cfc5d46834","target":"graph","created_at":"2026-07-05T10:36:18Z","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/2503.16370/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the $SL(2, \\mathbb{C})$ character variety of a Seifert-fibered homology $3$-sphere from the point of view of gauge theory. Namely, we introduce a class of perturbations of the $SL(2,\\mathbb{C})$ Chern--Simons functional and prove a localisation result: the perturbed critical points either approach a compact subset of the $SL(2, \\mathbb{C})$ character variety or else `escape to infinity'. Furthermore, the Euler characteristic and Poincar\\'e polynomial of the stable locus of the character variety are obtained by suitably counting the localising critical points.\n  As an application, we o","authors_text":"Juan Mu\\~noz-Ech\\'aniz","cross_cats":["math.AG","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-03-20T17:28:38Z","title":"Counting $SL(2,\\mathbb{C})$ connections on Seifert-fibered spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.16370","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":"sha256:36e2521f7919ba92f96cbb82afe3c8d82d9fc7f17d672b2abfabf5a0c0616042","target":"record","created_at":"2026-07-05T10:36:18Z","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":"2db0a4c7c364727e8a310c430cfdbc6620e5f5c2329b41f29002e54ea80bd6df","cross_cats_sorted":["math.AG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-03-20T17:28:38Z","title_canon_sha256":"6f5556890b99608e3c6b306637aeb85e1f23d44e0bc17eb8ef2b049ebdf2144a"},"schema_version":"1.0","source":{"id":"2503.16370","kind":"arxiv","version":1}},"canonical_sha256":"9d0dec4a5cbcd76d6ace8530bda02b64aec5200e55ce097bcb9a4f4b4dd2525e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d0dec4a5cbcd76d6ace8530bda02b64aec5200e55ce097bcb9a4f4b4dd2525e","first_computed_at":"2026-07-05T10:36:18.216415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:36:18.216415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eRdaONKPhxdhpsu2zma1iDNh5CLmVke60Nn1clsJUC6yLZQuNeAsz6hDa169TMwR0+4T6wp4b5sUlE3O9oNZBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:36:18.217118Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.16370","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36e2521f7919ba92f96cbb82afe3c8d82d9fc7f17d672b2abfabf5a0c0616042","sha256:881283a367722975498d9d2b5de2923e46dd9329a8c759e6c81274cfc5d46834"],"state_sha256":"5d096b6fc83f38e3fd8b0fa7d6af27509389966be22c4fa0aee01ca5cb1fef2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+52PsJVgjIX6r86wUkY+fXUmumOS8qCfrOcnhrBgT6Zeumelwvz1Dgfzd/5MEFk7BDlxcfRtZlq3a8NQc4XqDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T01:34:46.923243Z","bundle_sha256":"879f62307129cfa5ced624df0fb7c151c9a9b8205c59711d73dc25e1b9e9d373"}}