{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:4YBKPE7EEXNCXIR74ZSWTYXMM5","short_pith_number":"pith:4YBKPE7E","canonical_record":{"source":{"id":"2112.10053","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-12-19T03:37:37Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"280f06c36b43e7f8e830f220f8a21d8f71b30d9b43d61fff8120d0557f9f7b35","abstract_canon_sha256":"eb49f3135242bbf1de712950a24faffec94b790d1bfc0ebff05c8c052a78c580"},"schema_version":"1.0"},"canonical_sha256":"e602a793e425da2ba23fe66569e2ec6774f5e2a6eebfca6b2dd1f5bc308afb90","source":{"kind":"arxiv","id":"2112.10053","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.10053","created_at":"2026-07-05T10:11:54Z"},{"alias_kind":"arxiv_version","alias_value":"2112.10053v2","created_at":"2026-07-05T10:11:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.10053","created_at":"2026-07-05T10:11:54Z"},{"alias_kind":"pith_short_12","alias_value":"4YBKPE7EEXNC","created_at":"2026-07-05T10:11:54Z"},{"alias_kind":"pith_short_16","alias_value":"4YBKPE7EEXNCXIR7","created_at":"2026-07-05T10:11:54Z"},{"alias_kind":"pith_short_8","alias_value":"4YBKPE7E","created_at":"2026-07-05T10:11:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:4YBKPE7EEXNCXIR74ZSWTYXMM5","target":"record","payload":{"canonical_record":{"source":{"id":"2112.10053","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-12-19T03:37:37Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"280f06c36b43e7f8e830f220f8a21d8f71b30d9b43d61fff8120d0557f9f7b35","abstract_canon_sha256":"eb49f3135242bbf1de712950a24faffec94b790d1bfc0ebff05c8c052a78c580"},"schema_version":"1.0"},"canonical_sha256":"e602a793e425da2ba23fe66569e2ec6774f5e2a6eebfca6b2dd1f5bc308afb90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:11:54.970927Z","signature_b64":"8O3e47KwjOU+Y4ZWigx60gTgSKiYQmf11g1mdRJr/VXZdiTtw9ouFl/YjyjiQzN6eOZiWvvf67ikbbuSLzz3AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e602a793e425da2ba23fe66569e2ec6774f5e2a6eebfca6b2dd1f5bc308afb90","last_reissued_at":"2026-07-05T10:11:54.970484Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:11:54.970484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.10053","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":"2026-07-05T10:11:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ldFLDJKyS4+R1GINv3t3N3x+QVbYjcvmTNjA2wx0pgqibKSgfQoKHu+ImV/frddw2j+0gmscS0T2CjsgA3vfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T11:59:07.210658Z"},"content_sha256":"313235b64a95c48b1050c0058ca2b84bca7fc978adbf0898371f83ca671808e9","schema_version":"1.0","event_id":"sha256:313235b64a95c48b1050c0058ca2b84bca7fc978adbf0898371f83ca671808e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:4YBKPE7EEXNCXIR74ZSWTYXMM5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohomological $\\chi$-independence for Higgs bundles and Gopakumar-Vafa invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Naoki Koseki, Tasuki Kinjo","submitted_at":"2021-12-19T03:37:37Z","abstract_excerpt":"The aim of this paper is two-fold: Firstly, we prove Toda's $\\chi$-independence conjecture for Gopakumar--Vafa invariants of arbitrary local curves. Secondly, following Davison's work, we introduce the BPS cohomology for moduli spaces of Higgs bundles of rank $r$ and Euler characteristic $\\chi$ which are not necessary coprime, and show that it does not depend on $\\chi$. This result extends the Hausel--Thaddeus conjecture on the $\\chi$-independence of E-polynomials proved by Mellit, Groechenig--Wyss--Ziegler and Yu in two ways: we obtain an isomorphism of mixed Hodge modules on the Hitchin base"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.10053","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/2112.10053/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":"2026-07-05T10:11:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"710153qJjTXSwMWwRsbXdGLW640hqaizYZw7X74j7DclvAmdC50k8V5bzKOc1mLg9qBW6d2unFuoRTS+UTJUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T11:59:07.211177Z"},"content_sha256":"b93d058c0ef6a1630a7376dce33229aed24f33e1caacab55a6f8e2a1088029ba","schema_version":"1.0","event_id":"sha256:b93d058c0ef6a1630a7376dce33229aed24f33e1caacab55a6f8e2a1088029ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4YBKPE7EEXNCXIR74ZSWTYXMM5/bundle.json","state_url":"https://pith.science/pith/4YBKPE7EEXNCXIR74ZSWTYXMM5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4YBKPE7EEXNCXIR74ZSWTYXMM5/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":"2026-08-09T11:59:07Z","links":{"resolver":"https://pith.science/pith/4YBKPE7EEXNCXIR74ZSWTYXMM5","bundle":"https://pith.science/pith/4YBKPE7EEXNCXIR74ZSWTYXMM5/bundle.json","state":"https://pith.science/pith/4YBKPE7EEXNCXIR74ZSWTYXMM5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4YBKPE7EEXNCXIR74ZSWTYXMM5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:4YBKPE7EEXNCXIR74ZSWTYXMM5","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":"eb49f3135242bbf1de712950a24faffec94b790d1bfc0ebff05c8c052a78c580","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-12-19T03:37:37Z","title_canon_sha256":"280f06c36b43e7f8e830f220f8a21d8f71b30d9b43d61fff8120d0557f9f7b35"},"schema_version":"1.0","source":{"id":"2112.10053","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.10053","created_at":"2026-07-05T10:11:54Z"},{"alias_kind":"arxiv_version","alias_value":"2112.10053v2","created_at":"2026-07-05T10:11:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.10053","created_at":"2026-07-05T10:11:54Z"},{"alias_kind":"pith_short_12","alias_value":"4YBKPE7EEXNC","created_at":"2026-07-05T10:11:54Z"},{"alias_kind":"pith_short_16","alias_value":"4YBKPE7EEXNCXIR7","created_at":"2026-07-05T10:11:54Z"},{"alias_kind":"pith_short_8","alias_value":"4YBKPE7E","created_at":"2026-07-05T10:11:54Z"}],"graph_snapshots":[{"event_id":"sha256:b93d058c0ef6a1630a7376dce33229aed24f33e1caacab55a6f8e2a1088029ba","target":"graph","created_at":"2026-07-05T10:11:54Z","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/2112.10053/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The aim of this paper is two-fold: Firstly, we prove Toda's $\\chi$-independence conjecture for Gopakumar--Vafa invariants of arbitrary local curves. Secondly, following Davison's work, we introduce the BPS cohomology for moduli spaces of Higgs bundles of rank $r$ and Euler characteristic $\\chi$ which are not necessary coprime, and show that it does not depend on $\\chi$. This result extends the Hausel--Thaddeus conjecture on the $\\chi$-independence of E-polynomials proved by Mellit, Groechenig--Wyss--Ziegler and Yu in two ways: we obtain an isomorphism of mixed Hodge modules on the Hitchin base","authors_text":"Naoki Koseki, Tasuki Kinjo","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-12-19T03:37:37Z","title":"Cohomological $\\chi$-independence for Higgs bundles and Gopakumar-Vafa invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.10053","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":"sha256:313235b64a95c48b1050c0058ca2b84bca7fc978adbf0898371f83ca671808e9","target":"record","created_at":"2026-07-05T10:11:54Z","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":"eb49f3135242bbf1de712950a24faffec94b790d1bfc0ebff05c8c052a78c580","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-12-19T03:37:37Z","title_canon_sha256":"280f06c36b43e7f8e830f220f8a21d8f71b30d9b43d61fff8120d0557f9f7b35"},"schema_version":"1.0","source":{"id":"2112.10053","kind":"arxiv","version":2}},"canonical_sha256":"e602a793e425da2ba23fe66569e2ec6774f5e2a6eebfca6b2dd1f5bc308afb90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e602a793e425da2ba23fe66569e2ec6774f5e2a6eebfca6b2dd1f5bc308afb90","first_computed_at":"2026-07-05T10:11:54.970484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:11:54.970484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8O3e47KwjOU+Y4ZWigx60gTgSKiYQmf11g1mdRJr/VXZdiTtw9ouFl/YjyjiQzN6eOZiWvvf67ikbbuSLzz3AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:11:54.970927Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.10053","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:313235b64a95c48b1050c0058ca2b84bca7fc978adbf0898371f83ca671808e9","sha256:b93d058c0ef6a1630a7376dce33229aed24f33e1caacab55a6f8e2a1088029ba"],"state_sha256":"7a949d924922e8105690c08cc145f06bc28426b52837b41684c077765a30e4fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EEEyacH/XxnuvHevxQ6Wnm9mgnzQqSzVhMG3r6MYHwEGnffRTfpxCrFYyd9oVCslcq9aMjjTY974W5gL2KSrAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T11:59:07.215665Z","bundle_sha256":"84b8cbe6995a35378186448eefa6533309693cd4b9ce8fcc036642c96447ce7e"}}