{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:AKWT2GCBNSZ5MXBGSW52DVNCHE","short_pith_number":"pith:AKWT2GCB","canonical_record":{"source":{"id":"0906.1697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-06-09T19:56:51Z","cross_cats_sorted":[],"title_canon_sha256":"b4947adea5b0f8eaf981841f009885c78db975deb8ddb11da608b86908e57967","abstract_canon_sha256":"ad9ff71cd9575829035cf43b8c87530ee1b42d0e5ab17024a6bef8d7272b5ae9"},"schema_version":"1.0"},"canonical_sha256":"02ad3d18416cb3d65c2695bba1d5a239081729121b1a6049fea077d228924895","source":{"kind":"arxiv","id":"0906.1697","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.1697","created_at":"2026-05-18T02:13:21Z"},{"alias_kind":"arxiv_version","alias_value":"0906.1697v2","created_at":"2026-05-18T02:13:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.1697","created_at":"2026-05-18T02:13:21Z"},{"alias_kind":"pith_short_12","alias_value":"AKWT2GCBNSZ5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"AKWT2GCBNSZ5MXBG","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"AKWT2GCB","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:AKWT2GCBNSZ5MXBGSW52DVNCHE","target":"record","payload":{"canonical_record":{"source":{"id":"0906.1697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-06-09T19:56:51Z","cross_cats_sorted":[],"title_canon_sha256":"b4947adea5b0f8eaf981841f009885c78db975deb8ddb11da608b86908e57967","abstract_canon_sha256":"ad9ff71cd9575829035cf43b8c87530ee1b42d0e5ab17024a6bef8d7272b5ae9"},"schema_version":"1.0"},"canonical_sha256":"02ad3d18416cb3d65c2695bba1d5a239081729121b1a6049fea077d228924895","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:21.295459Z","signature_b64":"qdB311aYrD7twi4Mtjb26pfUZzKsfsFmPEvR6BaVwHtn8i0874aONoqxtjoJoH+MjlxpgExgJ8wkdschbiiMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02ad3d18416cb3d65c2695bba1d5a239081729121b1a6049fea077d228924895","last_reissued_at":"2026-05-18T02:13:21.294980Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:21.294980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.1697","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":"2026-05-18T02:13:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DN9dhRV1csNTX5lQDRbwEBkuRLZUXOcNWIu7YQW3jNZiSW5BJcYs/kJbYaprPmZj0hsV9WAetZvrKVRJXR3eBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:45:26.114684Z"},"content_sha256":"d9c932da36c8607e647923244ccc494fc254f49f11a597891d8b0a585aab7183","schema_version":"1.0","event_id":"sha256:d9c932da36c8607e647923244ccc494fc254f49f11a597891d8b0a585aab7183"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:AKWT2GCBNSZ5MXBGSW52DVNCHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Whittaker-Hill equation and semifinite-gap Schroedinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"A.D. Hemery, A.P. Veselov","submitted_at":"2009-06-09T19:56:51Z","abstract_excerpt":"A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by applying Darboux transformations to the Whittaker-Hill equation. We give a criterion of the regularity of the corresponding potentials and investigate the spectral properties of the new operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.1697","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":"2026-05-18T02:13:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W8t0WxvIxlBW0JpbicIFwl1gOD1notJbJVQHIS+vedNMV2PuV/5L+YLfrFbaiEozv4ztWmlCdU4+Zhqdjd6xCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:45:26.115020Z"},"content_sha256":"b9d96f69b4138fd687cb6a1f5b5f5923b0fd3fe5d417d6f8c5673edd38425399","schema_version":"1.0","event_id":"sha256:b9d96f69b4138fd687cb6a1f5b5f5923b0fd3fe5d417d6f8c5673edd38425399"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AKWT2GCBNSZ5MXBGSW52DVNCHE/bundle.json","state_url":"https://pith.science/pith/AKWT2GCBNSZ5MXBGSW52DVNCHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AKWT2GCBNSZ5MXBGSW52DVNCHE/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":"2026-06-02T21:45:26Z","links":{"resolver":"https://pith.science/pith/AKWT2GCBNSZ5MXBGSW52DVNCHE","bundle":"https://pith.science/pith/AKWT2GCBNSZ5MXBGSW52DVNCHE/bundle.json","state":"https://pith.science/pith/AKWT2GCBNSZ5MXBGSW52DVNCHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AKWT2GCBNSZ5MXBGSW52DVNCHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:AKWT2GCBNSZ5MXBGSW52DVNCHE","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":"ad9ff71cd9575829035cf43b8c87530ee1b42d0e5ab17024a6bef8d7272b5ae9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-06-09T19:56:51Z","title_canon_sha256":"b4947adea5b0f8eaf981841f009885c78db975deb8ddb11da608b86908e57967"},"schema_version":"1.0","source":{"id":"0906.1697","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.1697","created_at":"2026-05-18T02:13:21Z"},{"alias_kind":"arxiv_version","alias_value":"0906.1697v2","created_at":"2026-05-18T02:13:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.1697","created_at":"2026-05-18T02:13:21Z"},{"alias_kind":"pith_short_12","alias_value":"AKWT2GCBNSZ5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"AKWT2GCBNSZ5MXBG","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"AKWT2GCB","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:b9d96f69b4138fd687cb6a1f5b5f5923b0fd3fe5d417d6f8c5673edd38425399","target":"graph","created_at":"2026-05-18T02:13:21Z","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":"A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by applying Darboux transformations to the Whittaker-Hill equation. We give a criterion of the regularity of the corresponding potentials and investigate the spectral properties of the new operators.","authors_text":"A.D. Hemery, A.P. Veselov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-06-09T19:56:51Z","title":"Whittaker-Hill equation and semifinite-gap Schroedinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.1697","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:d9c932da36c8607e647923244ccc494fc254f49f11a597891d8b0a585aab7183","target":"record","created_at":"2026-05-18T02:13:21Z","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":"ad9ff71cd9575829035cf43b8c87530ee1b42d0e5ab17024a6bef8d7272b5ae9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-06-09T19:56:51Z","title_canon_sha256":"b4947adea5b0f8eaf981841f009885c78db975deb8ddb11da608b86908e57967"},"schema_version":"1.0","source":{"id":"0906.1697","kind":"arxiv","version":2}},"canonical_sha256":"02ad3d18416cb3d65c2695bba1d5a239081729121b1a6049fea077d228924895","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02ad3d18416cb3d65c2695bba1d5a239081729121b1a6049fea077d228924895","first_computed_at":"2026-05-18T02:13:21.294980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:21.294980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qdB311aYrD7twi4Mtjb26pfUZzKsfsFmPEvR6BaVwHtn8i0874aONoqxtjoJoH+MjlxpgExgJ8wkdschbiiMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:21.295459Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.1697","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9c932da36c8607e647923244ccc494fc254f49f11a597891d8b0a585aab7183","sha256:b9d96f69b4138fd687cb6a1f5b5f5923b0fd3fe5d417d6f8c5673edd38425399"],"state_sha256":"85d4471c5d1e18f7aed710cd7fefca392e64695eaca80006a3058a413751641c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ADoyVpeBgBY2oFLLAYYmLPORec5kjHvPL+v4rOXJKp3FwhEr3SX28losZC7AwydwY7PFwzARr+X56t2fhcJSBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:45:26.117001Z","bundle_sha256":"cf463942ef8e5dbf171ca942c0c0c9c9da56211cf30c6fc4cc009fb163fff3f8"}}