{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZNMGOBSMZB6AUNXTKJMJISTMA3","short_pith_number":"pith:ZNMGOBSM","canonical_record":{"source":{"id":"1210.0835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-10-02T16:37:33Z","cross_cats_sorted":["math-ph","math.CO","math.FA","math.MP"],"title_canon_sha256":"3d5588f5086f4108a53a82bfb806b6dccffce6452df984283ef9c09ae08cb25e","abstract_canon_sha256":"137de280021c400e99256d1c91943c1eddef8ed4442bdfe7fe8da708897a0b5c"},"schema_version":"1.0"},"canonical_sha256":"cb5867064cc87c0a36f35258944a6c06da3f5098816e7539f5386f2418e1749e","source":{"kind":"arxiv","id":"1210.0835","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0835","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0835v1","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0835","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"pith_short_12","alias_value":"ZNMGOBSMZB6A","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZNMGOBSMZB6AUNXT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZNMGOBSM","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZNMGOBSMZB6AUNXTKJMJISTMA3","target":"record","payload":{"canonical_record":{"source":{"id":"1210.0835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-10-02T16:37:33Z","cross_cats_sorted":["math-ph","math.CO","math.FA","math.MP"],"title_canon_sha256":"3d5588f5086f4108a53a82bfb806b6dccffce6452df984283ef9c09ae08cb25e","abstract_canon_sha256":"137de280021c400e99256d1c91943c1eddef8ed4442bdfe7fe8da708897a0b5c"},"schema_version":"1.0"},"canonical_sha256":"cb5867064cc87c0a36f35258944a6c06da3f5098816e7539f5386f2418e1749e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:14.160614Z","signature_b64":"fv4zEPJrAud7xIGQ10DQvCmXEY9azl6+tspXd1+TrZpeMd6kD2ANtT8XKGQ4fgwGPfZIKyFafA08dvg9FInXCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb5867064cc87c0a36f35258944a6c06da3f5098816e7539f5386f2418e1749e","last_reissued_at":"2026-05-18T03:44:14.160155Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:14.160155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.0835","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":"2026-05-18T03:44:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4mQdTJApH+yzxpbJfJbIT6Cw7RCpKHXmk8nm7YxC28ZZyu3EmYh4oB1/lqnd575zfI/11rsi/3MxQXNuemYLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:01:42.474217Z"},"content_sha256":"41a5472a7b0f6a8ae57e1b0abf8ec60cc4a723526e635ba3d9d9596b02cf9937","schema_version":"1.0","event_id":"sha256:41a5472a7b0f6a8ae57e1b0abf8ec60cc4a723526e635ba3d9d9596b02cf9937"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZNMGOBSMZB6AUNXTKJMJISTMA3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combinatorial identities related to eigenfunction decompositions of Hill operators: Open Questions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Boris Mityagin, Plamen Djakov","submitted_at":"2012-10-02T16:37:33Z","abstract_excerpt":"We formulate several open questions related to enumerative combinatorics, which arise in the spectral analysis of Hill operators with trigonometric polynomial potentials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0835","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":""},"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":"2026-05-18T03:44:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JC6/rLmcuMIBsS7IIppWwPsrnkynuGaJ4122tYwnjdVweL8VK9oE72dT3m8kJBjcf70STgmfyXLq/qX4ghbsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:01:42.474572Z"},"content_sha256":"effb5b36333ac895f3670b768d04387f07ebc852f14534f9c7f1a8da68456c82","schema_version":"1.0","event_id":"sha256:effb5b36333ac895f3670b768d04387f07ebc852f14534f9c7f1a8da68456c82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZNMGOBSMZB6AUNXTKJMJISTMA3/bundle.json","state_url":"https://pith.science/pith/ZNMGOBSMZB6AUNXTKJMJISTMA3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZNMGOBSMZB6AUNXTKJMJISTMA3/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":"2026-05-28T04:01:42Z","links":{"resolver":"https://pith.science/pith/ZNMGOBSMZB6AUNXTKJMJISTMA3","bundle":"https://pith.science/pith/ZNMGOBSMZB6AUNXTKJMJISTMA3/bundle.json","state":"https://pith.science/pith/ZNMGOBSMZB6AUNXTKJMJISTMA3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZNMGOBSMZB6AUNXTKJMJISTMA3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZNMGOBSMZB6AUNXTKJMJISTMA3","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":"137de280021c400e99256d1c91943c1eddef8ed4442bdfe7fe8da708897a0b5c","cross_cats_sorted":["math-ph","math.CO","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-10-02T16:37:33Z","title_canon_sha256":"3d5588f5086f4108a53a82bfb806b6dccffce6452df984283ef9c09ae08cb25e"},"schema_version":"1.0","source":{"id":"1210.0835","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0835","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0835v1","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0835","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"pith_short_12","alias_value":"ZNMGOBSMZB6A","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZNMGOBSMZB6AUNXT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZNMGOBSM","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:effb5b36333ac895f3670b768d04387f07ebc852f14534f9c7f1a8da68456c82","target":"graph","created_at":"2026-05-18T03:44:14Z","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":"We formulate several open questions related to enumerative combinatorics, which arise in the spectral analysis of Hill operators with trigonometric polynomial potentials.","authors_text":"Boris Mityagin, Plamen Djakov","cross_cats":["math-ph","math.CO","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-10-02T16:37:33Z","title":"Combinatorial identities related to eigenfunction decompositions of Hill operators: Open Questions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0835","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":"sha256:41a5472a7b0f6a8ae57e1b0abf8ec60cc4a723526e635ba3d9d9596b02cf9937","target":"record","created_at":"2026-05-18T03:44:14Z","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":"137de280021c400e99256d1c91943c1eddef8ed4442bdfe7fe8da708897a0b5c","cross_cats_sorted":["math-ph","math.CO","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-10-02T16:37:33Z","title_canon_sha256":"3d5588f5086f4108a53a82bfb806b6dccffce6452df984283ef9c09ae08cb25e"},"schema_version":"1.0","source":{"id":"1210.0835","kind":"arxiv","version":1}},"canonical_sha256":"cb5867064cc87c0a36f35258944a6c06da3f5098816e7539f5386f2418e1749e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb5867064cc87c0a36f35258944a6c06da3f5098816e7539f5386f2418e1749e","first_computed_at":"2026-05-18T03:44:14.160155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:14.160155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fv4zEPJrAud7xIGQ10DQvCmXEY9azl6+tspXd1+TrZpeMd6kD2ANtT8XKGQ4fgwGPfZIKyFafA08dvg9FInXCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:14.160614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.0835","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41a5472a7b0f6a8ae57e1b0abf8ec60cc4a723526e635ba3d9d9596b02cf9937","sha256:effb5b36333ac895f3670b768d04387f07ebc852f14534f9c7f1a8da68456c82"],"state_sha256":"cae6e8091ca7bb2eac9d0af13f2dddcaa57c8b1289beaba4a28aac5a0225ee09"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"958EHV2oMDINTKx3lMmvvlsr1mXeCznToABSaSYRSQIpcdqQjuvxVS8nSl2UHnlg6PRgjCeLkAQ1UrZAkqkCAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T04:01:42.476544Z","bundle_sha256":"9582aa704ff4db6c86484bdd67b40f50abcd6d16cbce61fb00225da8117644c1"}}