{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AK7ITH4KFQLMOJEXTDQ2E5Q53S","short_pith_number":"pith:AK7ITH4K","canonical_record":{"source":{"id":"1506.03651","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-06-11T12:40:38Z","cross_cats_sorted":[],"title_canon_sha256":"44edf33f929051a875289f6d1ef4e78c812e3bea3f528e7b425e56c4e7307d1f","abstract_canon_sha256":"6c43e7d8be460ae633624190e0602364222d27d026244e8babb7c46af2f9f26c"},"schema_version":"1.0"},"canonical_sha256":"02be899f8a2c16c7249798e1a2761ddc8faa61534660b665e0bd77774849a10c","source":{"kind":"arxiv","id":"1506.03651","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03651","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03651v2","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03651","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"AK7ITH4KFQLM","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AK7ITH4KFQLMOJEX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AK7ITH4K","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AK7ITH4KFQLMOJEXTDQ2E5Q53S","target":"record","payload":{"canonical_record":{"source":{"id":"1506.03651","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-06-11T12:40:38Z","cross_cats_sorted":[],"title_canon_sha256":"44edf33f929051a875289f6d1ef4e78c812e3bea3f528e7b425e56c4e7307d1f","abstract_canon_sha256":"6c43e7d8be460ae633624190e0602364222d27d026244e8babb7c46af2f9f26c"},"schema_version":"1.0"},"canonical_sha256":"02be899f8a2c16c7249798e1a2761ddc8faa61534660b665e0bd77774849a10c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:47.398663Z","signature_b64":"xtviwIlzEYXjwoZEfsrO6/t6xt0v/S0AfOjH2sO3hM4UZgB7JgvwGq9k7WqXPU3KN4R5ebg+p1m1GY9Ulo1ODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02be899f8a2c16c7249798e1a2761ddc8faa61534660b665e0bd77774849a10c","last_reissued_at":"2026-05-17T23:50:47.398030Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:47.398030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.03651","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":"2026-05-17T23:50:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y2ZrpPs6iwbqFCFF7ky9YBQ8f7CNAgh3NCb3SsW/fEY9WrzClbdZg1HzGlvKAA8/wD0zdwQSELyzApAkMzCtAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:09:57.187311Z"},"content_sha256":"14813b1db21bc98d77277d6482002262a5f6a666076f36e5398256df5a6fe186","schema_version":"1.0","event_id":"sha256:14813b1db21bc98d77277d6482002262a5f6a666076f36e5398256df5a6fe186"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AK7ITH4KFQLMOJEXTDQ2E5Q53S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recurrence Relations for Exceptional Hermite Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A.B.J. Kuijlaars, A. Kasman, D. Gomez-Ullate, R. Milson","submitted_at":"2015-06-11T12:40:38Z","abstract_excerpt":"The bispectral anti-isomorphism is applied to differential operators involving elements of the stabilizer ring to produce explicit formulas for all difference operators having any of the Hermite exceptional orthogonal polynomials as eigenfunctions with eigenvalues that are polynomials in $x$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03651","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":""},"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":"2026-05-17T23:50:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JTbJ6O33zEownd2pANN1YOjncbpjKl8LBxsjXVrbuzmzQyUpkQXn5ISbSNd06NKT0ioKAyq7U5rWhCXGM1rnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:09:57.187689Z"},"content_sha256":"076acf105681302ccb86d4056eb1dab99d4f99a049caddefaaa5c84d3d0d27dd","schema_version":"1.0","event_id":"sha256:076acf105681302ccb86d4056eb1dab99d4f99a049caddefaaa5c84d3d0d27dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AK7ITH4KFQLMOJEXTDQ2E5Q53S/bundle.json","state_url":"https://pith.science/pith/AK7ITH4KFQLMOJEXTDQ2E5Q53S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AK7ITH4KFQLMOJEXTDQ2E5Q53S/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":"2026-05-30T04:09:57Z","links":{"resolver":"https://pith.science/pith/AK7ITH4KFQLMOJEXTDQ2E5Q53S","bundle":"https://pith.science/pith/AK7ITH4KFQLMOJEXTDQ2E5Q53S/bundle.json","state":"https://pith.science/pith/AK7ITH4KFQLMOJEXTDQ2E5Q53S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AK7ITH4KFQLMOJEXTDQ2E5Q53S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AK7ITH4KFQLMOJEXTDQ2E5Q53S","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":"6c43e7d8be460ae633624190e0602364222d27d026244e8babb7c46af2f9f26c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-06-11T12:40:38Z","title_canon_sha256":"44edf33f929051a875289f6d1ef4e78c812e3bea3f528e7b425e56c4e7307d1f"},"schema_version":"1.0","source":{"id":"1506.03651","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03651","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03651v2","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03651","created_at":"2026-05-17T23:50:47Z"},{"alias_kind":"pith_short_12","alias_value":"AK7ITH4KFQLM","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AK7ITH4KFQLMOJEX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AK7ITH4K","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:076acf105681302ccb86d4056eb1dab99d4f99a049caddefaaa5c84d3d0d27dd","target":"graph","created_at":"2026-05-17T23:50:47Z","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":"The bispectral anti-isomorphism is applied to differential operators involving elements of the stabilizer ring to produce explicit formulas for all difference operators having any of the Hermite exceptional orthogonal polynomials as eigenfunctions with eigenvalues that are polynomials in $x$.","authors_text":"A.B.J. Kuijlaars, A. Kasman, D. Gomez-Ullate, R. Milson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-06-11T12:40:38Z","title":"Recurrence Relations for Exceptional Hermite Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03651","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":"sha256:14813b1db21bc98d77277d6482002262a5f6a666076f36e5398256df5a6fe186","target":"record","created_at":"2026-05-17T23:50:47Z","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":"6c43e7d8be460ae633624190e0602364222d27d026244e8babb7c46af2f9f26c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-06-11T12:40:38Z","title_canon_sha256":"44edf33f929051a875289f6d1ef4e78c812e3bea3f528e7b425e56c4e7307d1f"},"schema_version":"1.0","source":{"id":"1506.03651","kind":"arxiv","version":2}},"canonical_sha256":"02be899f8a2c16c7249798e1a2761ddc8faa61534660b665e0bd77774849a10c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02be899f8a2c16c7249798e1a2761ddc8faa61534660b665e0bd77774849a10c","first_computed_at":"2026-05-17T23:50:47.398030Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:47.398030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xtviwIlzEYXjwoZEfsrO6/t6xt0v/S0AfOjH2sO3hM4UZgB7JgvwGq9k7WqXPU3KN4R5ebg+p1m1GY9Ulo1ODg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:47.398663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03651","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14813b1db21bc98d77277d6482002262a5f6a666076f36e5398256df5a6fe186","sha256:076acf105681302ccb86d4056eb1dab99d4f99a049caddefaaa5c84d3d0d27dd"],"state_sha256":"0399e6a270a37cf64e68b85bafdf4a82a4a1c195a166e2228176371cfff29665"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/cxTSfudgkxmU9zxVl/Yt083k0LOmnxYqxQhKIYwcN1WjCKqO+gDONFrcqovqY5kr9xjnbud5hAtIOkLRv3gCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T04:09:57.189913Z","bundle_sha256":"a64cf9a43b710f428e8d4f6a1ee86000964cedf5ddb69a9e4eb36efabc7c91c9"}}