{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YCBYIRW6FID2U7F7QMHAL7SUOK","short_pith_number":"pith:YCBYIRW6","canonical_record":{"source":{"id":"1311.1396","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-06T13:59:06Z","cross_cats_sorted":["math-ph","math.MP","math.NT","nlin.CD"],"title_canon_sha256":"b2ec718af0fd85353d22ad2c7764b4685f237400bcc62421d53204dd64e1498e","abstract_canon_sha256":"60755580c42256a660e0b3abb3c97fc3a8cc16fdf353d5801bcda79881fa8620"},"schema_version":"1.0"},"canonical_sha256":"c0838446de2a07aa7cbf830e05fe5472ba6be993237c62f1159662b573ba27dd","source":{"kind":"arxiv","id":"1311.1396","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1396","created_at":"2026-05-18T02:55:57Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1396v2","created_at":"2026-05-18T02:55:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1396","created_at":"2026-05-18T02:55:57Z"},{"alias_kind":"pith_short_12","alias_value":"YCBYIRW6FID2","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YCBYIRW6FID2U7F7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YCBYIRW6","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YCBYIRW6FID2U7F7QMHAL7SUOK","target":"record","payload":{"canonical_record":{"source":{"id":"1311.1396","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-06T13:59:06Z","cross_cats_sorted":["math-ph","math.MP","math.NT","nlin.CD"],"title_canon_sha256":"b2ec718af0fd85353d22ad2c7764b4685f237400bcc62421d53204dd64e1498e","abstract_canon_sha256":"60755580c42256a660e0b3abb3c97fc3a8cc16fdf353d5801bcda79881fa8620"},"schema_version":"1.0"},"canonical_sha256":"c0838446de2a07aa7cbf830e05fe5472ba6be993237c62f1159662b573ba27dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:57.144198Z","signature_b64":"xY4v+mXk2abZ1F+3fmtpkZzhLvegrUHKJhXnd13CM9hBkK95PX7YkvHK0snFpZeqYDK6W8BmMyR8T4VpvyRsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0838446de2a07aa7cbf830e05fe5472ba6be993237c62f1159662b573ba27dd","last_reissued_at":"2026-05-18T02:55:57.143557Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:57.143557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.1396","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":"2026-05-18T02:55:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rtjWYXBnBnVrXlCEgreZyyp9KSlKb3cLjdhB0BnhQEWbICsZMoVTMGwdRCzngbjlPfuIOouJ3HOfB64ehPypDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:41:54.559141Z"},"content_sha256":"1cd5d12ca8c3de42610e6191dd9b1a0182ee0921dbfb94c2a43d6783704eeae1","schema_version":"1.0","event_id":"sha256:1cd5d12ca8c3de42610e6191dd9b1a0182ee0921dbfb94c2a43d6783704eeae1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YCBYIRW6FID2U7F7QMHAL7SUOK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Ergodicity for Point Scatterers on Arithmetic Tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.NT","nlin.CD"],"primary_cat":"math.AP","authors_text":"Henrik Ueberschaer, Par Kurlberg","submitted_at":"2013-11-06T13:59:06Z","abstract_excerpt":"We prove an analogue of Shnirelman, Zelditch and Colin de Verdiere's Quantum Ergodicity Theorems in a case where there is no underlying classical ergodicity. The system we consider is the Laplacian with a delta potential on the square torus. There are two types of wave functions: old eigenfunctions of the Laplacian, which are not affected by the scatterer, and new eigenfunctions which have a logarithmic singularity at the position of the scatterer. We prove that a full density subsequence of the new eigenfunctions equidistribute in phase space. Our estimates are uniform with respect to the cou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1396","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":"2026-05-18T02:55:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7gXeihtxrMmJsIE8DADZ2a1YdtSOPoYGkbtVgRZ2b3s/E/3XxI0XGvPFTwEsCR1zkbCRBYx57RYCqY+L15MrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:41:54.559520Z"},"content_sha256":"87da16d16df3442dffc0d4cc7619b50b71838c374c609dda80b9c6a5b3bb266b","schema_version":"1.0","event_id":"sha256:87da16d16df3442dffc0d4cc7619b50b71838c374c609dda80b9c6a5b3bb266b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YCBYIRW6FID2U7F7QMHAL7SUOK/bundle.json","state_url":"https://pith.science/pith/YCBYIRW6FID2U7F7QMHAL7SUOK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YCBYIRW6FID2U7F7QMHAL7SUOK/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":"2026-06-05T00:41:54Z","links":{"resolver":"https://pith.science/pith/YCBYIRW6FID2U7F7QMHAL7SUOK","bundle":"https://pith.science/pith/YCBYIRW6FID2U7F7QMHAL7SUOK/bundle.json","state":"https://pith.science/pith/YCBYIRW6FID2U7F7QMHAL7SUOK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YCBYIRW6FID2U7F7QMHAL7SUOK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YCBYIRW6FID2U7F7QMHAL7SUOK","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":"60755580c42256a660e0b3abb3c97fc3a8cc16fdf353d5801bcda79881fa8620","cross_cats_sorted":["math-ph","math.MP","math.NT","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-06T13:59:06Z","title_canon_sha256":"b2ec718af0fd85353d22ad2c7764b4685f237400bcc62421d53204dd64e1498e"},"schema_version":"1.0","source":{"id":"1311.1396","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1396","created_at":"2026-05-18T02:55:57Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1396v2","created_at":"2026-05-18T02:55:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1396","created_at":"2026-05-18T02:55:57Z"},{"alias_kind":"pith_short_12","alias_value":"YCBYIRW6FID2","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YCBYIRW6FID2U7F7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YCBYIRW6","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:87da16d16df3442dffc0d4cc7619b50b71838c374c609dda80b9c6a5b3bb266b","target":"graph","created_at":"2026-05-18T02:55:57Z","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 an analogue of Shnirelman, Zelditch and Colin de Verdiere's Quantum Ergodicity Theorems in a case where there is no underlying classical ergodicity. The system we consider is the Laplacian with a delta potential on the square torus. There are two types of wave functions: old eigenfunctions of the Laplacian, which are not affected by the scatterer, and new eigenfunctions which have a logarithmic singularity at the position of the scatterer. We prove that a full density subsequence of the new eigenfunctions equidistribute in phase space. Our estimates are uniform with respect to the cou","authors_text":"Henrik Ueberschaer, Par Kurlberg","cross_cats":["math-ph","math.MP","math.NT","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-06T13:59:06Z","title":"Quantum Ergodicity for Point Scatterers on Arithmetic Tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1396","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":"sha256:1cd5d12ca8c3de42610e6191dd9b1a0182ee0921dbfb94c2a43d6783704eeae1","target":"record","created_at":"2026-05-18T02:55:57Z","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":"60755580c42256a660e0b3abb3c97fc3a8cc16fdf353d5801bcda79881fa8620","cross_cats_sorted":["math-ph","math.MP","math.NT","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-06T13:59:06Z","title_canon_sha256":"b2ec718af0fd85353d22ad2c7764b4685f237400bcc62421d53204dd64e1498e"},"schema_version":"1.0","source":{"id":"1311.1396","kind":"arxiv","version":2}},"canonical_sha256":"c0838446de2a07aa7cbf830e05fe5472ba6be993237c62f1159662b573ba27dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0838446de2a07aa7cbf830e05fe5472ba6be993237c62f1159662b573ba27dd","first_computed_at":"2026-05-18T02:55:57.143557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:57.143557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xY4v+mXk2abZ1F+3fmtpkZzhLvegrUHKJhXnd13CM9hBkK95PX7YkvHK0snFpZeqYDK6W8BmMyR8T4VpvyRsAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:57.144198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.1396","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cd5d12ca8c3de42610e6191dd9b1a0182ee0921dbfb94c2a43d6783704eeae1","sha256:87da16d16df3442dffc0d4cc7619b50b71838c374c609dda80b9c6a5b3bb266b"],"state_sha256":"e3bc14544ebd2c6040a0573a9265a8300763d3651b1c0e4e4451ad0be0ce1526"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WYipkWJvxAqIGbXoyQWJMAQLeLTmgCAeZVVbjrhX1ElNhcYF4mSXZBw55yYDbpB/gcGu5uHfYq8Qmxt5lHw8CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T00:41:54.561741Z","bundle_sha256":"06e61584c24308256b6582da9a97045664db046050b1b1963d9da1f888254a85"}}