{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FQCBZFM2DGNE4OHO56QWCLEPTP","short_pith_number":"pith:FQCBZFM2","canonical_record":{"source":{"id":"1303.4055","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-17T12:04:35Z","cross_cats_sorted":["math.CA","math.MP","math.SP"],"title_canon_sha256":"46d17880ea8d4cf00ddf998e43a0db8d4978fcef0c3506b34ffc2852a10d95b0","abstract_canon_sha256":"07bffdd406890c3025ddf0ab2cab3f72c156dddfeffe5e418740e73f6bcc27a0"},"schema_version":"1.0"},"canonical_sha256":"2c041c959a199a4e38eeefa1612c8f9bdae026eeedc7a681b01b0ffd393d0f97","source":{"kind":"arxiv","id":"1303.4055","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4055","created_at":"2026-05-18T03:19:04Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4055v1","created_at":"2026-05-18T03:19:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4055","created_at":"2026-05-18T03:19:04Z"},{"alias_kind":"pith_short_12","alias_value":"FQCBZFM2DGNE","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FQCBZFM2DGNE4OHO","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FQCBZFM2","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FQCBZFM2DGNE4OHO56QWCLEPTP","target":"record","payload":{"canonical_record":{"source":{"id":"1303.4055","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-17T12:04:35Z","cross_cats_sorted":["math.CA","math.MP","math.SP"],"title_canon_sha256":"46d17880ea8d4cf00ddf998e43a0db8d4978fcef0c3506b34ffc2852a10d95b0","abstract_canon_sha256":"07bffdd406890c3025ddf0ab2cab3f72c156dddfeffe5e418740e73f6bcc27a0"},"schema_version":"1.0"},"canonical_sha256":"2c041c959a199a4e38eeefa1612c8f9bdae026eeedc7a681b01b0ffd393d0f97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:04.283063Z","signature_b64":"1mKlsEZKHrU3L6sX+f0s939G6LYyt6h1LpE+IIkNBkR6Ja4ySm7G9L/O8VZAH4GElMyFFgMQmFnizjgvtrIKAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c041c959a199a4e38eeefa1612c8f9bdae026eeedc7a681b01b0ffd393d0f97","last_reissued_at":"2026-05-18T03:19:04.282410Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:04.282410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.4055","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":"2026-05-18T03:19:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Irp8A49tXEQhDfXDrdg0g+M6hm0OhhYO8F0Seb5aps7Umwwi2wBDki7OiKNGPkY5/Hb0dG6ZTyHT9zdARWoRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:08:52.547965Z"},"content_sha256":"f2aef6521a2941d1103cd01b7543fc8df5d42e37d583774373fb42548dae81d3","schema_version":"1.0","event_id":"sha256:f2aef6521a2941d1103cd01b7543fc8df5d42e37d583774373fb42548dae81d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FQCBZFM2DGNE4OHO56QWCLEPTP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"1-D Schr\\\"odinger operators with local point interactions: a review","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Aleksey Kostenko, Mark Malamud","submitted_at":"2013-03-17T12:04:35Z","abstract_excerpt":"We review recent developments in the theory of 1-D Schr\\\"odinger operators with local point interactions on a discrete set. The progress in this area was stimulated by recent advances in the extension theory of symmetric operators and in the theory of ordinary differential operators with distributional coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4055","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":"2026-05-18T03:19:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k+MVV8+QYp/OxiYLtDFbGrgKxPLYQQitANNl9RreUWS9hUFWdi7NvHdEgsdtHecwAdnOy1liARAErYjOhF3LAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:08:52.548334Z"},"content_sha256":"40f4f3a777d74a73960ab56e1f16d1fdf6c8c25f174b663ac27dd0c5e313c9e1","schema_version":"1.0","event_id":"sha256:40f4f3a777d74a73960ab56e1f16d1fdf6c8c25f174b663ac27dd0c5e313c9e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FQCBZFM2DGNE4OHO56QWCLEPTP/bundle.json","state_url":"https://pith.science/pith/FQCBZFM2DGNE4OHO56QWCLEPTP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FQCBZFM2DGNE4OHO56QWCLEPTP/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":"2026-05-28T12:08:52Z","links":{"resolver":"https://pith.science/pith/FQCBZFM2DGNE4OHO56QWCLEPTP","bundle":"https://pith.science/pith/FQCBZFM2DGNE4OHO56QWCLEPTP/bundle.json","state":"https://pith.science/pith/FQCBZFM2DGNE4OHO56QWCLEPTP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FQCBZFM2DGNE4OHO56QWCLEPTP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FQCBZFM2DGNE4OHO56QWCLEPTP","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":"07bffdd406890c3025ddf0ab2cab3f72c156dddfeffe5e418740e73f6bcc27a0","cross_cats_sorted":["math.CA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-17T12:04:35Z","title_canon_sha256":"46d17880ea8d4cf00ddf998e43a0db8d4978fcef0c3506b34ffc2852a10d95b0"},"schema_version":"1.0","source":{"id":"1303.4055","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4055","created_at":"2026-05-18T03:19:04Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4055v1","created_at":"2026-05-18T03:19:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4055","created_at":"2026-05-18T03:19:04Z"},{"alias_kind":"pith_short_12","alias_value":"FQCBZFM2DGNE","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FQCBZFM2DGNE4OHO","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FQCBZFM2","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:40f4f3a777d74a73960ab56e1f16d1fdf6c8c25f174b663ac27dd0c5e313c9e1","target":"graph","created_at":"2026-05-18T03:19:04Z","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 review recent developments in the theory of 1-D Schr\\\"odinger operators with local point interactions on a discrete set. The progress in this area was stimulated by recent advances in the extension theory of symmetric operators and in the theory of ordinary differential operators with distributional coefficients.","authors_text":"Aleksey Kostenko, Mark Malamud","cross_cats":["math.CA","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-17T12:04:35Z","title":"1-D Schr\\\"odinger operators with local point interactions: a review"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4055","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:f2aef6521a2941d1103cd01b7543fc8df5d42e37d583774373fb42548dae81d3","target":"record","created_at":"2026-05-18T03:19:04Z","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":"07bffdd406890c3025ddf0ab2cab3f72c156dddfeffe5e418740e73f6bcc27a0","cross_cats_sorted":["math.CA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-17T12:04:35Z","title_canon_sha256":"46d17880ea8d4cf00ddf998e43a0db8d4978fcef0c3506b34ffc2852a10d95b0"},"schema_version":"1.0","source":{"id":"1303.4055","kind":"arxiv","version":1}},"canonical_sha256":"2c041c959a199a4e38eeefa1612c8f9bdae026eeedc7a681b01b0ffd393d0f97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c041c959a199a4e38eeefa1612c8f9bdae026eeedc7a681b01b0ffd393d0f97","first_computed_at":"2026-05-18T03:19:04.282410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:04.282410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1mKlsEZKHrU3L6sX+f0s939G6LYyt6h1LpE+IIkNBkR6Ja4ySm7G9L/O8VZAH4GElMyFFgMQmFnizjgvtrIKAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:04.283063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4055","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2aef6521a2941d1103cd01b7543fc8df5d42e37d583774373fb42548dae81d3","sha256:40f4f3a777d74a73960ab56e1f16d1fdf6c8c25f174b663ac27dd0c5e313c9e1"],"state_sha256":"c8943e2abb6995be577087c4aecff81aa6706b3ccce1f0ca72cfeddd1af29373"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PTALa9Li2JqG3pWfs6RUj152aiLdlzF7tjt8lVkoJk5ZvZ7jmtLHK40WdEqhQ59MnHDXg49WSA8VtBKy7zgPBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:08:52.550286Z","bundle_sha256":"d6cf1c21aea1939b2a5bb33c55ae9d32a51767994b0d8ae160d170d1c5c6e62c"}}