{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:AXEMN2PLAN7YRPB3R3Q2BPLLYM","short_pith_number":"pith:AXEMN2PL","canonical_record":{"source":{"id":"1109.0967","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-09-05T17:25:15Z","cross_cats_sorted":["math-ph","math.AP","math.CA","math.MP"],"title_canon_sha256":"429ca59d579775dd76c6f398f0bc1ee72a9679ed5aed015bc429c8e0d199e5e7","abstract_canon_sha256":"6f33abf2eaf3212e952ecc2f82a87e17b99c1c7b009c9f770a06ffb6af583cea"},"schema_version":"1.0"},"canonical_sha256":"05c8c6e9eb037f88bc3b8ee1a0bd6bc301e0c92f72c3986749d27b2b6773e0ef","source":{"kind":"arxiv","id":"1109.0967","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0967","created_at":"2026-05-18T02:00:39Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0967v1","created_at":"2026-05-18T02:00:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0967","created_at":"2026-05-18T02:00:39Z"},{"alias_kind":"pith_short_12","alias_value":"AXEMN2PLAN7Y","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AXEMN2PLAN7YRPB3","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AXEMN2PL","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:AXEMN2PLAN7YRPB3R3Q2BPLLYM","target":"record","payload":{"canonical_record":{"source":{"id":"1109.0967","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-09-05T17:25:15Z","cross_cats_sorted":["math-ph","math.AP","math.CA","math.MP"],"title_canon_sha256":"429ca59d579775dd76c6f398f0bc1ee72a9679ed5aed015bc429c8e0d199e5e7","abstract_canon_sha256":"6f33abf2eaf3212e952ecc2f82a87e17b99c1c7b009c9f770a06ffb6af583cea"},"schema_version":"1.0"},"canonical_sha256":"05c8c6e9eb037f88bc3b8ee1a0bd6bc301e0c92f72c3986749d27b2b6773e0ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:39.597877Z","signature_b64":"sJqs2hQ+au+95UH+XVYq6jLgqxBCz2MZcyRhzA9Ag8TBMJ5Fun+ZJA5hjFZGE4iOlK8HEfV4UZWvIOn113+tCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05c8c6e9eb037f88bc3b8ee1a0bd6bc301e0c92f72c3986749d27b2b6773e0ef","last_reissued_at":"2026-05-18T02:00:39.597231Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:39.597231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.0967","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":"2026-05-18T02:00:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"72HxRAchcs55oMf3/A/a5vT7Hg8EIwrG2HM7b9D/LFu4Y4WeSaCZHoTFlMF207DxrgLH26H/3O3xs11P/oPgDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:51:32.674381Z"},"content_sha256":"9ec615e1bae9273a5c26183a956b5c0a315deb57e5216c4ae446fb98fe1308bb","schema_version":"1.0","event_id":"sha256:9ec615e1bae9273a5c26183a956b5c0a315deb57e5216c4ae446fb98fe1308bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:AXEMN2PLAN7YRPB3R3Q2BPLLYM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Fulling-Kuchment theorem for the 1D harmonic oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.CA","math.MP"],"primary_cat":"math.SP","authors_text":"Hamid Hezari, Victor Guillemin","submitted_at":"2011-09-05T17:25:15Z","abstract_excerpt":"We prove that there exists a pair of \"non-isospectral\" 1D semiclassical Schr\\\"odinger operators whose spectra agree modulo h^\\infty. In particular, all their semiclassical trace invariants are the same. Our proof is based on an idea of Fulling-Kuchment and Hadamard's variational formula applied to suitable perturbations of the harmonic oscillator.\n  Keywords: Inverse spectral problems, semiclassical Schr\\\"odinger operators, trace invariants, Hadamard's variational formula, harmonic oscillator, Penrose mushroom, Sturm-Liouville theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0967","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":"2026-05-18T02:00:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FiFFY/wWr3Im3DAgVO5WrkPAmVQUICs7x1wnLGfvkz/Om3T5B7j7nnxQ6xz0YCdG5r7plNoHt4ausQV72WIZCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:51:32.675125Z"},"content_sha256":"851ad34b0fc54262539b9674ef7c634b98a4884ed35ea88c86b55767e79b3976","schema_version":"1.0","event_id":"sha256:851ad34b0fc54262539b9674ef7c634b98a4884ed35ea88c86b55767e79b3976"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AXEMN2PLAN7YRPB3R3Q2BPLLYM/bundle.json","state_url":"https://pith.science/pith/AXEMN2PLAN7YRPB3R3Q2BPLLYM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AXEMN2PLAN7YRPB3R3Q2BPLLYM/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":"2026-06-10T23:51:32Z","links":{"resolver":"https://pith.science/pith/AXEMN2PLAN7YRPB3R3Q2BPLLYM","bundle":"https://pith.science/pith/AXEMN2PLAN7YRPB3R3Q2BPLLYM/bundle.json","state":"https://pith.science/pith/AXEMN2PLAN7YRPB3R3Q2BPLLYM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AXEMN2PLAN7YRPB3R3Q2BPLLYM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:AXEMN2PLAN7YRPB3R3Q2BPLLYM","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":"6f33abf2eaf3212e952ecc2f82a87e17b99c1c7b009c9f770a06ffb6af583cea","cross_cats_sorted":["math-ph","math.AP","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-09-05T17:25:15Z","title_canon_sha256":"429ca59d579775dd76c6f398f0bc1ee72a9679ed5aed015bc429c8e0d199e5e7"},"schema_version":"1.0","source":{"id":"1109.0967","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0967","created_at":"2026-05-18T02:00:39Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0967v1","created_at":"2026-05-18T02:00:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0967","created_at":"2026-05-18T02:00:39Z"},{"alias_kind":"pith_short_12","alias_value":"AXEMN2PLAN7Y","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AXEMN2PLAN7YRPB3","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AXEMN2PL","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:851ad34b0fc54262539b9674ef7c634b98a4884ed35ea88c86b55767e79b3976","target":"graph","created_at":"2026-05-18T02:00:39Z","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 prove that there exists a pair of \"non-isospectral\" 1D semiclassical Schr\\\"odinger operators whose spectra agree modulo h^\\infty. In particular, all their semiclassical trace invariants are the same. Our proof is based on an idea of Fulling-Kuchment and Hadamard's variational formula applied to suitable perturbations of the harmonic oscillator.\n  Keywords: Inverse spectral problems, semiclassical Schr\\\"odinger operators, trace invariants, Hadamard's variational formula, harmonic oscillator, Penrose mushroom, Sturm-Liouville theory.","authors_text":"Hamid Hezari, Victor Guillemin","cross_cats":["math-ph","math.AP","math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-09-05T17:25:15Z","title":"A Fulling-Kuchment theorem for the 1D harmonic oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0967","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":"sha256:9ec615e1bae9273a5c26183a956b5c0a315deb57e5216c4ae446fb98fe1308bb","target":"record","created_at":"2026-05-18T02:00:39Z","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":"6f33abf2eaf3212e952ecc2f82a87e17b99c1c7b009c9f770a06ffb6af583cea","cross_cats_sorted":["math-ph","math.AP","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-09-05T17:25:15Z","title_canon_sha256":"429ca59d579775dd76c6f398f0bc1ee72a9679ed5aed015bc429c8e0d199e5e7"},"schema_version":"1.0","source":{"id":"1109.0967","kind":"arxiv","version":1}},"canonical_sha256":"05c8c6e9eb037f88bc3b8ee1a0bd6bc301e0c92f72c3986749d27b2b6773e0ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05c8c6e9eb037f88bc3b8ee1a0bd6bc301e0c92f72c3986749d27b2b6773e0ef","first_computed_at":"2026-05-18T02:00:39.597231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:39.597231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sJqs2hQ+au+95UH+XVYq6jLgqxBCz2MZcyRhzA9Ag8TBMJ5Fun+ZJA5hjFZGE4iOlK8HEfV4UZWvIOn113+tCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:39.597877Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0967","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ec615e1bae9273a5c26183a956b5c0a315deb57e5216c4ae446fb98fe1308bb","sha256:851ad34b0fc54262539b9674ef7c634b98a4884ed35ea88c86b55767e79b3976"],"state_sha256":"741f522aaad03f7a1dc8f224d21ab6473f3cb8f6db23acb5132af1d3bfba291c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PeGCvX3LJA1o1HFfCbtKty/9AB+IdGyjUDCeRKv1aGy+qOs4Q2wJbO7qeJRYETIxOETLEWZQtcVi2UEkOg8VDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:51:32.679107Z","bundle_sha256":"5e1459910149968f264c71eaee3f91df8b8d9b0185b66e4e6d8d0987cee0f429"}}