{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:BLIO7UM5IQ5PHVRFZJJRWA5GJU","short_pith_number":"pith:BLIO7UM5","canonical_record":{"source":{"id":"2607.00359","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-07-01T02:57:09Z","cross_cats_sorted":[],"title_canon_sha256":"7a8085eea4a1831d78937a2347ad27d2a65846d4341bf75cafc22346ce8fee5b","abstract_canon_sha256":"4ec2b1038f59737a70a0fa4304266988db032ad3892ef054336ff6d99a674a8f"},"schema_version":"1.0"},"canonical_sha256":"0ad0efd19d443af3d625ca531b03a64d38c05148403584e8c3eb36edb388dca8","source":{"kind":"arxiv","id":"2607.00359","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00359","created_at":"2026-07-02T01:17:41Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00359v1","created_at":"2026-07-02T01:17:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00359","created_at":"2026-07-02T01:17:41Z"},{"alias_kind":"pith_short_12","alias_value":"BLIO7UM5IQ5P","created_at":"2026-07-02T01:17:41Z"},{"alias_kind":"pith_short_16","alias_value":"BLIO7UM5IQ5PHVRF","created_at":"2026-07-02T01:17:41Z"},{"alias_kind":"pith_short_8","alias_value":"BLIO7UM5","created_at":"2026-07-02T01:17:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:BLIO7UM5IQ5PHVRFZJJRWA5GJU","target":"record","payload":{"canonical_record":{"source":{"id":"2607.00359","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-07-01T02:57:09Z","cross_cats_sorted":[],"title_canon_sha256":"7a8085eea4a1831d78937a2347ad27d2a65846d4341bf75cafc22346ce8fee5b","abstract_canon_sha256":"4ec2b1038f59737a70a0fa4304266988db032ad3892ef054336ff6d99a674a8f"},"schema_version":"1.0"},"canonical_sha256":"0ad0efd19d443af3d625ca531b03a64d38c05148403584e8c3eb36edb388dca8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:17:41.106625Z","signature_b64":"dleoqY1Y2HJ71XfVqTn7Izt4jVvRCAAFL1AtzpJ4Ym+IMGgegP4Z6GDeGAcVBYwgg4vcZS+MWPfssT2rN4LkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ad0efd19d443af3d625ca531b03a64d38c05148403584e8c3eb36edb388dca8","last_reissued_at":"2026-07-02T01:17:41.106180Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:17:41.106180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.00359","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":"2026-07-02T01:17:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"14Pc6ngQxoQcgKFmOo7M2trVinX3tYdTUDd/k1X9c4ILwd2QrbZoOavCoIIAI2UuMc1N11/Eejlt8iTrzWaZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T15:46:56.081520Z"},"content_sha256":"86742e90229ab3bcc79c4590800eebc947258379e313f0896fb9d8456d0080cd","schema_version":"1.0","event_id":"sha256:86742e90229ab3bcc79c4590800eebc947258379e313f0896fb9d8456d0080cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:BLIO7UM5IQ5PHVRFZJJRWA5GJU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Equivalence Problem for Generalized Airy Operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ruichen Qiu, Ruyong Feng, Yichuan Cao, Yunfei Li","submitted_at":"2026-07-01T02:57:09Z","abstract_excerpt":"In this paper, we establish degree obstructions to the equivalence of generalized Airy operators of the same type. As an application, we answer a question posed by Nicholas M. Katz in Inventiones Mathematicae (87, pp. 13-61,1987). The main results of Sections 3 and 4 were obtained through a close interactive collaboration between the authors and the artificial intelligence agent system MechMath Agent Team (MMAT)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00359","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/2607.00359/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":"2026-07-02T01:17:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ds2LBxSwovS8QbaOuYhYzra9wOBdkjFwY0dFDPwm7LnqpmwOEHhobkXh5YyDp3JXfZLmBJ55iKyKJxcnygDEBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T15:46:56.081880Z"},"content_sha256":"3ec379dc127b5ba81daba2e71bf9c6f9a6569030a8d8b677b9ac6d3f21596ccb","schema_version":"1.0","event_id":"sha256:3ec379dc127b5ba81daba2e71bf9c6f9a6569030a8d8b677b9ac6d3f21596ccb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BLIO7UM5IQ5PHVRFZJJRWA5GJU/bundle.json","state_url":"https://pith.science/pith/BLIO7UM5IQ5PHVRFZJJRWA5GJU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BLIO7UM5IQ5PHVRFZJJRWA5GJU/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":"2026-07-03T15:46:56Z","links":{"resolver":"https://pith.science/pith/BLIO7UM5IQ5PHVRFZJJRWA5GJU","bundle":"https://pith.science/pith/BLIO7UM5IQ5PHVRFZJJRWA5GJU/bundle.json","state":"https://pith.science/pith/BLIO7UM5IQ5PHVRFZJJRWA5GJU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BLIO7UM5IQ5PHVRFZJJRWA5GJU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BLIO7UM5IQ5PHVRFZJJRWA5GJU","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":"4ec2b1038f59737a70a0fa4304266988db032ad3892ef054336ff6d99a674a8f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-07-01T02:57:09Z","title_canon_sha256":"7a8085eea4a1831d78937a2347ad27d2a65846d4341bf75cafc22346ce8fee5b"},"schema_version":"1.0","source":{"id":"2607.00359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00359","created_at":"2026-07-02T01:17:41Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00359v1","created_at":"2026-07-02T01:17:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00359","created_at":"2026-07-02T01:17:41Z"},{"alias_kind":"pith_short_12","alias_value":"BLIO7UM5IQ5P","created_at":"2026-07-02T01:17:41Z"},{"alias_kind":"pith_short_16","alias_value":"BLIO7UM5IQ5PHVRF","created_at":"2026-07-02T01:17:41Z"},{"alias_kind":"pith_short_8","alias_value":"BLIO7UM5","created_at":"2026-07-02T01:17:41Z"}],"graph_snapshots":[{"event_id":"sha256:3ec379dc127b5ba81daba2e71bf9c6f9a6569030a8d8b677b9ac6d3f21596ccb","target":"graph","created_at":"2026-07-02T01:17:41Z","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/2607.00359/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we establish degree obstructions to the equivalence of generalized Airy operators of the same type. As an application, we answer a question posed by Nicholas M. Katz in Inventiones Mathematicae (87, pp. 13-61,1987). The main results of Sections 3 and 4 were obtained through a close interactive collaboration between the authors and the artificial intelligence agent system MechMath Agent Team (MMAT).","authors_text":"Ruichen Qiu, Ruyong Feng, Yichuan Cao, Yunfei Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-07-01T02:57:09Z","title":"The Equivalence Problem for Generalized Airy Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00359","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":"sha256:86742e90229ab3bcc79c4590800eebc947258379e313f0896fb9d8456d0080cd","target":"record","created_at":"2026-07-02T01:17:41Z","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":"4ec2b1038f59737a70a0fa4304266988db032ad3892ef054336ff6d99a674a8f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-07-01T02:57:09Z","title_canon_sha256":"7a8085eea4a1831d78937a2347ad27d2a65846d4341bf75cafc22346ce8fee5b"},"schema_version":"1.0","source":{"id":"2607.00359","kind":"arxiv","version":1}},"canonical_sha256":"0ad0efd19d443af3d625ca531b03a64d38c05148403584e8c3eb36edb388dca8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ad0efd19d443af3d625ca531b03a64d38c05148403584e8c3eb36edb388dca8","first_computed_at":"2026-07-02T01:17:41.106180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T01:17:41.106180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dleoqY1Y2HJ71XfVqTn7Izt4jVvRCAAFL1AtzpJ4Ym+IMGgegP4Z6GDeGAcVBYwgg4vcZS+MWPfssT2rN4LkCw==","signature_status":"signed_v1","signed_at":"2026-07-02T01:17:41.106625Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.00359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86742e90229ab3bcc79c4590800eebc947258379e313f0896fb9d8456d0080cd","sha256:3ec379dc127b5ba81daba2e71bf9c6f9a6569030a8d8b677b9ac6d3f21596ccb"],"state_sha256":"4dfc3edd74f298e9846bd7cbe988bae5c676002c4a235fe3520de1e3abd0cca6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ayc5KLzJau4sINWr4nnL1mI9PG8Ha42m/emo127WYd8bfZCe06xXDa4DvYnN+wTHpS504S/FbsJ6+aZmW+4yCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T15:46:56.083858Z","bundle_sha256":"28b7ab47e41f1a58df04bc43183ca27a5378cb725c2357196b0e119740690b25"}}