{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:VPGU6STE6X5JKC3HPLARWBTRSI","short_pith_number":"pith:VPGU6STE","canonical_record":{"source":{"id":"2411.07487","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-12T02:16:26Z","cross_cats_sorted":[],"title_canon_sha256":"5cecd12b12b17fe635614acf99dab499e9d9e06e1fd65263b93d9a7d5c52c4c7","abstract_canon_sha256":"842c3cfdc35ba9853754d9ddfdd52417d833c52bab67317eb585e5ffacf577dd"},"schema_version":"1.0"},"canonical_sha256":"abcd4f4a64f5fa950b677ac11b0671920084212f61181244f3816811928b986f","source":{"kind":"arxiv","id":"2411.07487","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.07487","created_at":"2026-07-05T10:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"2411.07487v2","created_at":"2026-07-05T10:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.07487","created_at":"2026-07-05T10:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"VPGU6STE6X5J","created_at":"2026-07-05T10:12:23Z"},{"alias_kind":"pith_short_16","alias_value":"VPGU6STE6X5JKC3H","created_at":"2026-07-05T10:12:23Z"},{"alias_kind":"pith_short_8","alias_value":"VPGU6STE","created_at":"2026-07-05T10:12:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:VPGU6STE6X5JKC3HPLARWBTRSI","target":"record","payload":{"canonical_record":{"source":{"id":"2411.07487","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-12T02:16:26Z","cross_cats_sorted":[],"title_canon_sha256":"5cecd12b12b17fe635614acf99dab499e9d9e06e1fd65263b93d9a7d5c52c4c7","abstract_canon_sha256":"842c3cfdc35ba9853754d9ddfdd52417d833c52bab67317eb585e5ffacf577dd"},"schema_version":"1.0"},"canonical_sha256":"abcd4f4a64f5fa950b677ac11b0671920084212f61181244f3816811928b986f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:12:23.384003Z","signature_b64":"AVrvWUBEACUEv2WtHa+Ccq3+pletLILSoh1VMhE5jdvsvfkEivdDBqVcS81zh2j9AL/RWP1ba1wFA09BExXeDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abcd4f4a64f5fa950b677ac11b0671920084212f61181244f3816811928b986f","last_reissued_at":"2026-07-05T10:12:23.383521Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:12:23.383521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.07487","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":"2026-07-05T10:12:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8aGvPKDfPHTAZe0VUZ1gRYX4iv86FPfI6HOCIFIvkozUUrrR+k9CLzWqWJ3BSSAMdi2DU88Az0yS5IwRN3eRDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:43:56.506504Z"},"content_sha256":"fa3fc66d6f83435a658691161e9c8e5bb66b61afe749855a599908c522afc539","schema_version":"1.0","event_id":"sha256:fa3fc66d6f83435a658691161e9c8e5bb66b61afe749855a599908c522afc539"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:VPGU6STE6X5JKC3HPLARWBTRSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two reconstruction theorems in permutation equivariant quantum K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dun Tang","submitted_at":"2024-11-12T02:16:26Z","abstract_excerpt":"In this paper, we first generalize the K-theoretic Ancestor-Descendant (AD) correspondence in \\cite{perm7} to allow arbitrary permutative inputs. With this version of AD correspondence, we reconstruct K-theoretical descendant $g=0$ invariants, and $g=1$ invariants with point target space, from $1$-point invariants of the corresponding genus. In the appendix, we show that the graph of big $\\mathcal{J}$ function also forms a Lagrangian cone in the permutation equivariant setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.07487","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/2411.07487/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":"2026-07-05T10:12:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2D4rdLHsDHH37tCVegI48sJKE358oxnNzc+GvuPaAxvM1c+BgtvVsbqzxZREtkoZvJTOOFG81KPTFsRe56DgCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:43:56.507296Z"},"content_sha256":"22b8bb0dc045eb043a35286f54eaa2cc65565b89662b5f78883ab547b03ad0b9","schema_version":"1.0","event_id":"sha256:22b8bb0dc045eb043a35286f54eaa2cc65565b89662b5f78883ab547b03ad0b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VPGU6STE6X5JKC3HPLARWBTRSI/bundle.json","state_url":"https://pith.science/pith/VPGU6STE6X5JKC3HPLARWBTRSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VPGU6STE6X5JKC3HPLARWBTRSI/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":"2026-08-09T19:43:56Z","links":{"resolver":"https://pith.science/pith/VPGU6STE6X5JKC3HPLARWBTRSI","bundle":"https://pith.science/pith/VPGU6STE6X5JKC3HPLARWBTRSI/bundle.json","state":"https://pith.science/pith/VPGU6STE6X5JKC3HPLARWBTRSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VPGU6STE6X5JKC3HPLARWBTRSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VPGU6STE6X5JKC3HPLARWBTRSI","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":"842c3cfdc35ba9853754d9ddfdd52417d833c52bab67317eb585e5ffacf577dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-12T02:16:26Z","title_canon_sha256":"5cecd12b12b17fe635614acf99dab499e9d9e06e1fd65263b93d9a7d5c52c4c7"},"schema_version":"1.0","source":{"id":"2411.07487","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.07487","created_at":"2026-07-05T10:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"2411.07487v2","created_at":"2026-07-05T10:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.07487","created_at":"2026-07-05T10:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"VPGU6STE6X5J","created_at":"2026-07-05T10:12:23Z"},{"alias_kind":"pith_short_16","alias_value":"VPGU6STE6X5JKC3H","created_at":"2026-07-05T10:12:23Z"},{"alias_kind":"pith_short_8","alias_value":"VPGU6STE","created_at":"2026-07-05T10:12:23Z"}],"graph_snapshots":[{"event_id":"sha256:22b8bb0dc045eb043a35286f54eaa2cc65565b89662b5f78883ab547b03ad0b9","target":"graph","created_at":"2026-07-05T10:12:23Z","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/2411.07487/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we first generalize the K-theoretic Ancestor-Descendant (AD) correspondence in \\cite{perm7} to allow arbitrary permutative inputs. With this version of AD correspondence, we reconstruct K-theoretical descendant $g=0$ invariants, and $g=1$ invariants with point target space, from $1$-point invariants of the corresponding genus. In the appendix, we show that the graph of big $\\mathcal{J}$ function also forms a Lagrangian cone in the permutation equivariant setting.","authors_text":"Dun Tang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-12T02:16:26Z","title":"Two reconstruction theorems in permutation equivariant quantum K-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.07487","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:fa3fc66d6f83435a658691161e9c8e5bb66b61afe749855a599908c522afc539","target":"record","created_at":"2026-07-05T10:12:23Z","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":"842c3cfdc35ba9853754d9ddfdd52417d833c52bab67317eb585e5ffacf577dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-12T02:16:26Z","title_canon_sha256":"5cecd12b12b17fe635614acf99dab499e9d9e06e1fd65263b93d9a7d5c52c4c7"},"schema_version":"1.0","source":{"id":"2411.07487","kind":"arxiv","version":2}},"canonical_sha256":"abcd4f4a64f5fa950b677ac11b0671920084212f61181244f3816811928b986f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abcd4f4a64f5fa950b677ac11b0671920084212f61181244f3816811928b986f","first_computed_at":"2026-07-05T10:12:23.383521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:12:23.383521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AVrvWUBEACUEv2WtHa+Ccq3+pletLILSoh1VMhE5jdvsvfkEivdDBqVcS81zh2j9AL/RWP1ba1wFA09BExXeDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:12:23.384003Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.07487","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa3fc66d6f83435a658691161e9c8e5bb66b61afe749855a599908c522afc539","sha256:22b8bb0dc045eb043a35286f54eaa2cc65565b89662b5f78883ab547b03ad0b9"],"state_sha256":"f8b79327418f8f31fb5bbe024cc72a4e72042d649d7e60be767f011aa4dd2017"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WL5RPdJD1eTKZpg6/nlxoigno5XgE9GvGE0kXSCV6CWjllzXl8I9QNVuVsuzpVxC2ZVG+8em0P5siJmbKm0oDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T19:43:56.512214Z","bundle_sha256":"ba25bffa558782e0b5233ee13bcb06bc82015a80e848f26a4ac289fdcbec91b6"}}