{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:JIBGCUKFLEJYKAKGHQYVPJYMBY","short_pith_number":"pith:JIBGCUKF","canonical_record":{"source":{"id":"2404.12531","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-04-18T22:23:53Z","cross_cats_sorted":[],"title_canon_sha256":"9c6866fa123a2b8d0c5ee95554ce75c830e5418ee7767de109bd723f2d9a211f","abstract_canon_sha256":"eff6ae016ba2cb2a25aea71c181c7554e6c5779924df38e5f17c6431e932146b"},"schema_version":"1.0"},"canonical_sha256":"4a0261514559138501463c3157a70c0e1d4a9f1ce7eb5ac7a19355821bb2e1c9","source":{"kind":"arxiv","id":"2404.12531","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.12531","created_at":"2026-07-05T08:09:54Z"},{"alias_kind":"arxiv_version","alias_value":"2404.12531v1","created_at":"2026-07-05T08:09:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.12531","created_at":"2026-07-05T08:09:54Z"},{"alias_kind":"pith_short_12","alias_value":"JIBGCUKFLEJY","created_at":"2026-07-05T08:09:54Z"},{"alias_kind":"pith_short_16","alias_value":"JIBGCUKFLEJYKAKG","created_at":"2026-07-05T08:09:54Z"},{"alias_kind":"pith_short_8","alias_value":"JIBGCUKF","created_at":"2026-07-05T08:09:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:JIBGCUKFLEJYKAKGHQYVPJYMBY","target":"record","payload":{"canonical_record":{"source":{"id":"2404.12531","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-04-18T22:23:53Z","cross_cats_sorted":[],"title_canon_sha256":"9c6866fa123a2b8d0c5ee95554ce75c830e5418ee7767de109bd723f2d9a211f","abstract_canon_sha256":"eff6ae016ba2cb2a25aea71c181c7554e6c5779924df38e5f17c6431e932146b"},"schema_version":"1.0"},"canonical_sha256":"4a0261514559138501463c3157a70c0e1d4a9f1ce7eb5ac7a19355821bb2e1c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:09:54.793658Z","signature_b64":"Y7VABMbm36Zgp5XqA81u6MtibuQalcDZeKsIx/aA+UZlGdcO8Xgtz4IaFjmh30vBITkQl6xmJFyGDWM4W1ySBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a0261514559138501463c3157a70c0e1d4a9f1ce7eb5ac7a19355821bb2e1c9","last_reissued_at":"2026-07-05T08:09:54.793221Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:09:54.793221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.12531","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":"2026-07-05T08:09:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sBrB7vczobGRNmX+umSBPxaKmadGpf02K+OtOnla0T6wDD0o4zucHaYO3gphGF5lot71ogYt8CzrkwqsWnauAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T06:53:41.307401Z"},"content_sha256":"2a5b5380927ef96ebe01d597b534bfcda4bf6770636b88a01cdd8ca2b1498c37","schema_version":"1.0","event_id":"sha256:2a5b5380927ef96ebe01d597b534bfcda4bf6770636b88a01cdd8ca2b1498c37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:JIBGCUKFLEJYKAKGHQYVPJYMBY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Essential self-adjointness of the Laplacian on weighted graphs: harmonic functions, stability, characterizations and capacity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Atsushi Inoue, Jun Masamune, Rados{\\l}aw K. Wojciechowski, Sean Ku","submitted_at":"2024-04-18T22:23:53Z","abstract_excerpt":"We give two characterizations for the essential self-adjointness of the weighted Laplacian on birth-death chains. The first involves the edge weights and vertex measure and is classically known; however, we give another proof using stability results, limit point-limit circle theory and the connection between essential self-adjointness and harmonic functions. The second characterization involves a new notion of capacity. Furthermore, we also analyze the essential self-adjointness of Schr\\\"odinger operators, use the characterizations for birth-death chains and stability results to characterize e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.12531","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.12531/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:09:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fvisuh8bSxWn2QtDcqmcp0Hc4i7h81lry3a8tXHuOXDns0jtCfCLnWW3JFOl0PdS6flGYmx9586pDyk3N86ZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T06:53:41.307780Z"},"content_sha256":"e0e5cb91ab4d5e8d01789c735cd3a08597d2a7d234e89d40d8d4a58d0a85e07d","schema_version":"1.0","event_id":"sha256:e0e5cb91ab4d5e8d01789c735cd3a08597d2a7d234e89d40d8d4a58d0a85e07d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JIBGCUKFLEJYKAKGHQYVPJYMBY/bundle.json","state_url":"https://pith.science/pith/JIBGCUKFLEJYKAKGHQYVPJYMBY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JIBGCUKFLEJYKAKGHQYVPJYMBY/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":"2026-07-07T06:53:41Z","links":{"resolver":"https://pith.science/pith/JIBGCUKFLEJYKAKGHQYVPJYMBY","bundle":"https://pith.science/pith/JIBGCUKFLEJYKAKGHQYVPJYMBY/bundle.json","state":"https://pith.science/pith/JIBGCUKFLEJYKAKGHQYVPJYMBY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JIBGCUKFLEJYKAKGHQYVPJYMBY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JIBGCUKFLEJYKAKGHQYVPJYMBY","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":"eff6ae016ba2cb2a25aea71c181c7554e6c5779924df38e5f17c6431e932146b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-04-18T22:23:53Z","title_canon_sha256":"9c6866fa123a2b8d0c5ee95554ce75c830e5418ee7767de109bd723f2d9a211f"},"schema_version":"1.0","source":{"id":"2404.12531","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.12531","created_at":"2026-07-05T08:09:54Z"},{"alias_kind":"arxiv_version","alias_value":"2404.12531v1","created_at":"2026-07-05T08:09:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.12531","created_at":"2026-07-05T08:09:54Z"},{"alias_kind":"pith_short_12","alias_value":"JIBGCUKFLEJY","created_at":"2026-07-05T08:09:54Z"},{"alias_kind":"pith_short_16","alias_value":"JIBGCUKFLEJYKAKG","created_at":"2026-07-05T08:09:54Z"},{"alias_kind":"pith_short_8","alias_value":"JIBGCUKF","created_at":"2026-07-05T08:09:54Z"}],"graph_snapshots":[{"event_id":"sha256:e0e5cb91ab4d5e8d01789c735cd3a08597d2a7d234e89d40d8d4a58d0a85e07d","target":"graph","created_at":"2026-07-05T08:09:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.12531/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give two characterizations for the essential self-adjointness of the weighted Laplacian on birth-death chains. The first involves the edge weights and vertex measure and is classically known; however, we give another proof using stability results, limit point-limit circle theory and the connection between essential self-adjointness and harmonic functions. The second characterization involves a new notion of capacity. Furthermore, we also analyze the essential self-adjointness of Schr\\\"odinger operators, use the characterizations for birth-death chains and stability results to characterize e","authors_text":"Atsushi Inoue, Jun Masamune, Rados{\\l}aw K. Wojciechowski, Sean Ku","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-04-18T22:23:53Z","title":"Essential self-adjointness of the Laplacian on weighted graphs: harmonic functions, stability, characterizations and capacity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.12531","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":"sha256:2a5b5380927ef96ebe01d597b534bfcda4bf6770636b88a01cdd8ca2b1498c37","target":"record","created_at":"2026-07-05T08:09:54Z","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":"eff6ae016ba2cb2a25aea71c181c7554e6c5779924df38e5f17c6431e932146b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-04-18T22:23:53Z","title_canon_sha256":"9c6866fa123a2b8d0c5ee95554ce75c830e5418ee7767de109bd723f2d9a211f"},"schema_version":"1.0","source":{"id":"2404.12531","kind":"arxiv","version":1}},"canonical_sha256":"4a0261514559138501463c3157a70c0e1d4a9f1ce7eb5ac7a19355821bb2e1c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a0261514559138501463c3157a70c0e1d4a9f1ce7eb5ac7a19355821bb2e1c9","first_computed_at":"2026-07-05T08:09:54.793221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:09:54.793221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y7VABMbm36Zgp5XqA81u6MtibuQalcDZeKsIx/aA+UZlGdcO8Xgtz4IaFjmh30vBITkQl6xmJFyGDWM4W1ySBA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:09:54.793658Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.12531","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a5b5380927ef96ebe01d597b534bfcda4bf6770636b88a01cdd8ca2b1498c37","sha256:e0e5cb91ab4d5e8d01789c735cd3a08597d2a7d234e89d40d8d4a58d0a85e07d"],"state_sha256":"a9ee2951a14babb49f52f0d19164db117848b4e6b6547e4a6d724a6b15fcdffa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H6x7A9uyIGHus2kvXPY2vH8z21/joFc1Ka7snQmgGo7838ugzkO4YyRQ9aozrd8BCbaroY5KuD8kGG0o476hBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T06:53:41.310029Z","bundle_sha256":"fa224184de3bbc653d052915f42849bfc160ece259305acd9c8fad8d7fd0dfd3"}}