{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B5GITG4BLM67V6HH4NN6VMOB6W","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":"d8431a875b04206d3b851d0140dbce02c75bfb430fbe5ecb8f8e225a612d20ca","cross_cats_sorted":["math.FA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-11-02T10:20:06Z","title_canon_sha256":"336bdded351136464689537ef068cb56ebca2f82b54d4701c15930dd01b6a011"},"schema_version":"1.0","source":{"id":"1211.0407","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0407","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0407v2","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0407","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"pith_short_12","alias_value":"B5GITG4BLM67","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B5GITG4BLM67V6HH","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B5GITG4B","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:ecff2efcbcf1729e25f00056543712b512a01ff2aaad85b10fc30db96f12697e","target":"graph","created_at":"2026-05-18T03:39:04Z","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":"Using the concept of intrinsic metric on a locally finite weighted graph, we give sufficient conditions for the magnetic Schr\\\"odinger operator to be essentially self-adjoint. The present paper is an extension of some recent results proven in the context of graphs of bounded degree.","authors_text":"Francoise Truc (IF), Ognjen Milatovic (UNF)","cross_cats":["math.FA","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-11-02T10:20:06Z","title":"Self-adjoint extensions of discrete magnetic Schr\\\"odinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0407","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":"sha256:5c0cdef81502dde66113993642452c14b32d880ec9a1ce192d0e8f38e6916e68","target":"record","created_at":"2026-05-18T03:39:04Z","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":"d8431a875b04206d3b851d0140dbce02c75bfb430fbe5ecb8f8e225a612d20ca","cross_cats_sorted":["math.FA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-11-02T10:20:06Z","title_canon_sha256":"336bdded351136464689537ef068cb56ebca2f82b54d4701c15930dd01b6a011"},"schema_version":"1.0","source":{"id":"1211.0407","kind":"arxiv","version":2}},"canonical_sha256":"0f4c899b815b3dfaf8e7e35beab1c1f58dbdcb4581dd9908175220c4b1e3b7a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f4c899b815b3dfaf8e7e35beab1c1f58dbdcb4581dd9908175220c4b1e3b7a4","first_computed_at":"2026-05-18T03:39:04.741737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:04.741737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wTXwiuh/VxO6fdY69e31Un6L7aYIgWt03C6/Tm9DVecmIAnshrnBe+LOeVNU5KMmXAYd9n7hpfyxjbklsKjvDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:04.742384Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0407","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c0cdef81502dde66113993642452c14b32d880ec9a1ce192d0e8f38e6916e68","sha256:ecff2efcbcf1729e25f00056543712b512a01ff2aaad85b10fc30db96f12697e"],"state_sha256":"332b15be60d8fe2ebefbf402fba8d051d6a58d33a000ef58b1a08b66dd27e255"}