{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TRRI2DDPPA5APLUKVRYJWZTANC","short_pith_number":"pith:TRRI2DDP","canonical_record":{"source":{"id":"1205.1944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-09T11:38:04Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d5e39a9084c8cc711b04d8196f4334734921b14a3bcbf119e0a54b5f70a6df61","abstract_canon_sha256":"19fb61b6b5ca131a7b48d7a02a532ec70a356a0a69f9ea43dfd935010dd3b0b1"},"schema_version":"1.0"},"canonical_sha256":"9c628d0c6f783a07ae8aac709b666068811ce8cc630bcdbf38bf65c6f633087b","source":{"kind":"arxiv","id":"1205.1944","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1944","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1944v1","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1944","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"TRRI2DDPPA5A","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TRRI2DDPPA5APLUK","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TRRI2DDP","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TRRI2DDPPA5APLUKVRYJWZTANC","target":"record","payload":{"canonical_record":{"source":{"id":"1205.1944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-09T11:38:04Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d5e39a9084c8cc711b04d8196f4334734921b14a3bcbf119e0a54b5f70a6df61","abstract_canon_sha256":"19fb61b6b5ca131a7b48d7a02a532ec70a356a0a69f9ea43dfd935010dd3b0b1"},"schema_version":"1.0"},"canonical_sha256":"9c628d0c6f783a07ae8aac709b666068811ce8cc630bcdbf38bf65c6f633087b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:42.307637Z","signature_b64":"QFUxXM68AKiRD68MmN/Q2+9gisVpAIhWcAqX0qnuaT1Ywmf98vlgxsMg+/bGZRX65oBWOcmrMbwTBDn1wF+lBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c628d0c6f783a07ae8aac709b666068811ce8cc630bcdbf38bf65c6f633087b","last_reissued_at":"2026-05-18T00:04:42.307076Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:42.307076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.1944","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":"2026-05-18T00:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MG5kbObWfWJLUC6ivlnHcxexj8HDCPxBUZ/KVTaUkACCxZ0/Tnc0amEujwTtZ7hmgVayOzgTI0CkmVHled3XDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:16:42.674784Z"},"content_sha256":"dcb356777ff30d4da4985d49ab2f84845954d8475510e8e4e8beecd181fcba03","schema_version":"1.0","event_id":"sha256:dcb356777ff30d4da4985d49ab2f84845954d8475510e8e4e8beecd181fcba03"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TRRI2DDPPA5APLUKVRYJWZTANC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unbounded quantum graphs with unbounded boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Carsten Schubert, Daniel Lenz, Ivan Veseli\\'c","submitted_at":"2012-05-09T11:38:04Z","abstract_excerpt":"We consider metric graphs with a uniform lower bound on the edge lengths but no further restrictions. We discuss how to describe every local self-adjoint Laplace operator on such graphs by boundary conditions in the vertices given by projections and self-adjoint operators. We then characterize the lower bounded self-adjoint Laplacians and determine their associated quadratic form in terms of the operator families encoding the boundary conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1944","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":"2026-05-18T00:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wrpMaVgNnx70MzovJta54Otmbq9WR1wny5YaZibef/HgPhbATTpsvTqXS4C/1kXMmF23o0eSLYm0vkUCNyjUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:16:42.675134Z"},"content_sha256":"9141c9589ba6d465183207c22cf44685bf522881e3df0c5c32e005178b8d6b1b","schema_version":"1.0","event_id":"sha256:9141c9589ba6d465183207c22cf44685bf522881e3df0c5c32e005178b8d6b1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TRRI2DDPPA5APLUKVRYJWZTANC/bundle.json","state_url":"https://pith.science/pith/TRRI2DDPPA5APLUKVRYJWZTANC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TRRI2DDPPA5APLUKVRYJWZTANC/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":"2026-06-01T16:16:42Z","links":{"resolver":"https://pith.science/pith/TRRI2DDPPA5APLUKVRYJWZTANC","bundle":"https://pith.science/pith/TRRI2DDPPA5APLUKVRYJWZTANC/bundle.json","state":"https://pith.science/pith/TRRI2DDPPA5APLUKVRYJWZTANC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TRRI2DDPPA5APLUKVRYJWZTANC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TRRI2DDPPA5APLUKVRYJWZTANC","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":"19fb61b6b5ca131a7b48d7a02a532ec70a356a0a69f9ea43dfd935010dd3b0b1","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-09T11:38:04Z","title_canon_sha256":"d5e39a9084c8cc711b04d8196f4334734921b14a3bcbf119e0a54b5f70a6df61"},"schema_version":"1.0","source":{"id":"1205.1944","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1944","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1944v1","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1944","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"TRRI2DDPPA5A","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TRRI2DDPPA5APLUK","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TRRI2DDP","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:9141c9589ba6d465183207c22cf44685bf522881e3df0c5c32e005178b8d6b1b","target":"graph","created_at":"2026-05-18T00:04:42Z","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 consider metric graphs with a uniform lower bound on the edge lengths but no further restrictions. We discuss how to describe every local self-adjoint Laplace operator on such graphs by boundary conditions in the vertices given by projections and self-adjoint operators. We then characterize the lower bounded self-adjoint Laplacians and determine their associated quadratic form in terms of the operator families encoding the boundary conditions.","authors_text":"Carsten Schubert, Daniel Lenz, Ivan Veseli\\'c","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-09T11:38:04Z","title":"Unbounded quantum graphs with unbounded boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1944","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:dcb356777ff30d4da4985d49ab2f84845954d8475510e8e4e8beecd181fcba03","target":"record","created_at":"2026-05-18T00:04:42Z","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":"19fb61b6b5ca131a7b48d7a02a532ec70a356a0a69f9ea43dfd935010dd3b0b1","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-09T11:38:04Z","title_canon_sha256":"d5e39a9084c8cc711b04d8196f4334734921b14a3bcbf119e0a54b5f70a6df61"},"schema_version":"1.0","source":{"id":"1205.1944","kind":"arxiv","version":1}},"canonical_sha256":"9c628d0c6f783a07ae8aac709b666068811ce8cc630bcdbf38bf65c6f633087b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c628d0c6f783a07ae8aac709b666068811ce8cc630bcdbf38bf65c6f633087b","first_computed_at":"2026-05-18T00:04:42.307076Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:42.307076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QFUxXM68AKiRD68MmN/Q2+9gisVpAIhWcAqX0qnuaT1Ywmf98vlgxsMg+/bGZRX65oBWOcmrMbwTBDn1wF+lBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:42.307637Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1944","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcb356777ff30d4da4985d49ab2f84845954d8475510e8e4e8beecd181fcba03","sha256:9141c9589ba6d465183207c22cf44685bf522881e3df0c5c32e005178b8d6b1b"],"state_sha256":"eca92b4197ef1b7e9ba91be669a35dd01cd1ae8b317614550ecf648391f64acb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sWAU/yEHRVGCwNl738C7KHSoYHmWUcsvJm4rV//zcF+y5i5GVhd2W44t9TLtFPxDvgC98Erm9AqeQQ+K3ZF7Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:16:42.677093Z","bundle_sha256":"44eae89867626cfc5e24a296cfac403dceed53c7ce9722231a69189848a06fe3"}}