{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IFVFBVN5NGEX3CBPMZWPXQLT7E","short_pith_number":"pith:IFVFBVN5","canonical_record":{"source":{"id":"1903.11810","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-03-28T07:15:40Z","cross_cats_sorted":[],"title_canon_sha256":"011e19a109163ed3b8976a475256fdeca73193aaf9207bf24424ab783ad26ef2","abstract_canon_sha256":"481786018e71f1192017cf47fc11e0d0daf0b0c4073b65ea239fde037c4665aa"},"schema_version":"1.0"},"canonical_sha256":"416a50d5bd69897d882f666cfbc173f92d9b0673e92fd1890b603fb8bc17ab07","source":{"kind":"arxiv","id":"1903.11810","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.11810","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"arxiv_version","alias_value":"1903.11810v1","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.11810","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"pith_short_12","alias_value":"IFVFBVN5NGEX","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IFVFBVN5NGEX3CBP","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IFVFBVN5","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IFVFBVN5NGEX3CBPMZWPXQLT7E","target":"record","payload":{"canonical_record":{"source":{"id":"1903.11810","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-03-28T07:15:40Z","cross_cats_sorted":[],"title_canon_sha256":"011e19a109163ed3b8976a475256fdeca73193aaf9207bf24424ab783ad26ef2","abstract_canon_sha256":"481786018e71f1192017cf47fc11e0d0daf0b0c4073b65ea239fde037c4665aa"},"schema_version":"1.0"},"canonical_sha256":"416a50d5bd69897d882f666cfbc173f92d9b0673e92fd1890b603fb8bc17ab07","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:59.046907Z","signature_b64":"pNZpN5jk8tawworvmvQSZAhIELSq1gKF17S7g74p4bFdnsKT/FmNflfEgLXWeaGApabZPqUxtVItrnHpLDLYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"416a50d5bd69897d882f666cfbc173f92d9b0673e92fd1890b603fb8bc17ab07","last_reissued_at":"2026-05-17T23:49:59.046347Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:59.046347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.11810","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":"2026-05-17T23:49:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o8b+JRUJZuWDWWbcjb0UrLZ7LomuLCuLLRvb/GV6JGzsPIQLtfGYdtuZUpshO4VOmKT7ZltBJBO3nNTqcAKACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:32:26.435667Z"},"content_sha256":"4c05fcee42607f435442767ddf4f17966dbc313189143bcaf5b5ca91f5cdef93","schema_version":"1.0","event_id":"sha256:4c05fcee42607f435442767ddf4f17966dbc313189143bcaf5b5ca91f5cdef93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IFVFBVN5NGEX3CBPMZWPXQLT7E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics and estimates of the discrete spectrum of the Schrodinger operator on a discrete periodic graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Evgeny Korotyaev, Vladimir Sloushch","submitted_at":"2019-03-28T07:15:40Z","abstract_excerpt":"The periodic Schrodinger operator $ H $ on a discrete periodic graph is considered. We estimate the discrete spectrum of the perturbed operator $ H _ {-} (t) = H-tV $, $ t> 0 $, where the potential $ V \\ ge 0 $ is decreasing and $t>0$ is the coupling constant. If the potential has a power asymptotics at infinity, then we obtain asymptotics of the discrete spectrum of operator $ H_ {-} (t) $ with a large coupling constant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11810","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":"2026-05-17T23:49:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cajo9NgRu14LKHjXRn6/+P/ynW+8T5GG8DcTEQT0Awi3Aq18z5CUkmQ36nW9yhSZ7SU2PukhDnR0/ydf8ctmAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:32:26.436347Z"},"content_sha256":"4c061d3157d91e9af40a93177cd51e54d736e9117dd08dbc7e5e4df7a246b2c7","schema_version":"1.0","event_id":"sha256:4c061d3157d91e9af40a93177cd51e54d736e9117dd08dbc7e5e4df7a246b2c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IFVFBVN5NGEX3CBPMZWPXQLT7E/bundle.json","state_url":"https://pith.science/pith/IFVFBVN5NGEX3CBPMZWPXQLT7E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IFVFBVN5NGEX3CBPMZWPXQLT7E/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":"2026-05-31T16:32:26Z","links":{"resolver":"https://pith.science/pith/IFVFBVN5NGEX3CBPMZWPXQLT7E","bundle":"https://pith.science/pith/IFVFBVN5NGEX3CBPMZWPXQLT7E/bundle.json","state":"https://pith.science/pith/IFVFBVN5NGEX3CBPMZWPXQLT7E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IFVFBVN5NGEX3CBPMZWPXQLT7E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IFVFBVN5NGEX3CBPMZWPXQLT7E","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":"481786018e71f1192017cf47fc11e0d0daf0b0c4073b65ea239fde037c4665aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-03-28T07:15:40Z","title_canon_sha256":"011e19a109163ed3b8976a475256fdeca73193aaf9207bf24424ab783ad26ef2"},"schema_version":"1.0","source":{"id":"1903.11810","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.11810","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"arxiv_version","alias_value":"1903.11810v1","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.11810","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"pith_short_12","alias_value":"IFVFBVN5NGEX","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IFVFBVN5NGEX3CBP","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IFVFBVN5","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:4c061d3157d91e9af40a93177cd51e54d736e9117dd08dbc7e5e4df7a246b2c7","target":"graph","created_at":"2026-05-17T23:49:59Z","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":"The periodic Schrodinger operator $ H $ on a discrete periodic graph is considered. We estimate the discrete spectrum of the perturbed operator $ H _ {-} (t) = H-tV $, $ t> 0 $, where the potential $ V \\ ge 0 $ is decreasing and $t>0$ is the coupling constant. If the potential has a power asymptotics at infinity, then we obtain asymptotics of the discrete spectrum of operator $ H_ {-} (t) $ with a large coupling constant.","authors_text":"Evgeny Korotyaev, Vladimir Sloushch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-03-28T07:15:40Z","title":"Asymptotics and estimates of the discrete spectrum of the Schrodinger operator on a discrete periodic graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11810","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":"sha256:4c05fcee42607f435442767ddf4f17966dbc313189143bcaf5b5ca91f5cdef93","target":"record","created_at":"2026-05-17T23:49:59Z","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":"481786018e71f1192017cf47fc11e0d0daf0b0c4073b65ea239fde037c4665aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-03-28T07:15:40Z","title_canon_sha256":"011e19a109163ed3b8976a475256fdeca73193aaf9207bf24424ab783ad26ef2"},"schema_version":"1.0","source":{"id":"1903.11810","kind":"arxiv","version":1}},"canonical_sha256":"416a50d5bd69897d882f666cfbc173f92d9b0673e92fd1890b603fb8bc17ab07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"416a50d5bd69897d882f666cfbc173f92d9b0673e92fd1890b603fb8bc17ab07","first_computed_at":"2026-05-17T23:49:59.046347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:59.046347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pNZpN5jk8tawworvmvQSZAhIELSq1gKF17S7g74p4bFdnsKT/FmNflfEgLXWeaGApabZPqUxtVItrnHpLDLYDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:59.046907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.11810","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c05fcee42607f435442767ddf4f17966dbc313189143bcaf5b5ca91f5cdef93","sha256:4c061d3157d91e9af40a93177cd51e54d736e9117dd08dbc7e5e4df7a246b2c7"],"state_sha256":"e96a298ee280118defec63b94be4e9a86646646f5d6aa4c8359771c8b60b2c8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KdzQjPWA5+x8f0hsr47eZMDe/rdQlpu5OX9F+4K3PSV5D5D8SHtTA9azDHu1mMtzrbQx0VOVmETPOYdU6DPEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:32:26.439752Z","bundle_sha256":"1c9dfed069e6d5b5b4383a525babbe342ba2aa2645bb21e6ee5f714b513563c1"}}