{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:M6H2BEZM6YM45VVEAIBEGX4TTO","short_pith_number":"pith:M6H2BEZM","canonical_record":{"source":{"id":"1309.5937","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-09-23T19:54:33Z","cross_cats_sorted":["math-ph","math.DG","math.FA","math.MP","math.PR"],"title_canon_sha256":"8de59af7b54b5d899bda5e60853ea9a6c2893ba6a214de9aa76d2c58dc2fbc71","abstract_canon_sha256":"e7ffa80bb60802d693410fd8aeabc3c02b54e5094aee2e63c20087de26dc2100"},"schema_version":"1.0"},"canonical_sha256":"678fa0932cf619ced6a40202435f939b9b9aac92f51aa646a6f6c6ffcc73fb29","source":{"kind":"arxiv","id":"1309.5937","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5937","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5937v2","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5937","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"M6H2BEZM6YM4","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"M6H2BEZM6YM45VVE","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"M6H2BEZM","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:M6H2BEZM6YM45VVEAIBEGX4TTO","target":"record","payload":{"canonical_record":{"source":{"id":"1309.5937","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-09-23T19:54:33Z","cross_cats_sorted":["math-ph","math.DG","math.FA","math.MP","math.PR"],"title_canon_sha256":"8de59af7b54b5d899bda5e60853ea9a6c2893ba6a214de9aa76d2c58dc2fbc71","abstract_canon_sha256":"e7ffa80bb60802d693410fd8aeabc3c02b54e5094aee2e63c20087de26dc2100"},"schema_version":"1.0"},"canonical_sha256":"678fa0932cf619ced6a40202435f939b9b9aac92f51aa646a6f6c6ffcc73fb29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:11.803368Z","signature_b64":"VuVEWqb245CD//lQsTheRN+uUk3ugTIT4LGmWhF7ZuQZKg8o61T5WyzM236A8pYYkj/1oyIUzUTycrVR1DhGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"678fa0932cf619ced6a40202435f939b9b9aac92f51aa646a6f6c6ffcc73fb29","last_reissued_at":"2026-05-18T00:12:11.802713Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:11.802713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.5937","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iC7V4p12BmcuUd+zD+qiAHfMck4JOpH9Ghqlh9PWi+zdoT2I4XOSq0TV1Ptif8mtyY4C3rrEI4L+f95NBYrMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:47:40.812486Z"},"content_sha256":"3166e4179d8a19356d9331a0ec93d98278ea89e3b4cf2ee1ef1a7611e298350c","schema_version":"1.0","event_id":"sha256:3166e4179d8a19356d9331a0ec93d98278ea89e3b4cf2ee1ef1a7611e298350c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:M6H2BEZM6YM45VVEAIBEGX4TTO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Metrics and spectral triples for Dirichlet and resistance forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.FA","math.MP","math.PR"],"primary_cat":"math.OA","authors_text":"Alexander Teplyaev, Daniel J. Kelleher, Michael Hinz","submitted_at":"2013-09-23T19:54:33Z","abstract_excerpt":"The article deals with intrinsic metrics, Dirac operators and spectral triples induced by regular Dirichlet and resistance forms. We show, in particular, that if a local resistance form is given and the space is compact in resistance metric, then the intrinsic metric yields a geodesic space. Given a regular Dirichlet form, we consider Dirac operators within the framework of differential 1-forms proposed by Cipriani and Sauvageot, and comment on its spectral properties. If the Dirichlet form admits a carr\\'e operator and the generator has discrete spectrum, then we can construct a related spect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5937","kind":"arxiv","version":2},"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":"2026-05-18T00:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GJRHO7BkWNf0kGPVMNCUxSc7BkKesb/1rYrr9ODSwxENv3XRng3mXQuSShITcvnpXbyQ9y4w/UEy4QhXr+GgDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:47:40.813227Z"},"content_sha256":"f5c648b281e1cd74b0a7edb9c456371ab939ab3b2d60633cd105b8ad470e8a94","schema_version":"1.0","event_id":"sha256:f5c648b281e1cd74b0a7edb9c456371ab939ab3b2d60633cd105b8ad470e8a94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6H2BEZM6YM45VVEAIBEGX4TTO/bundle.json","state_url":"https://pith.science/pith/M6H2BEZM6YM45VVEAIBEGX4TTO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6H2BEZM6YM45VVEAIBEGX4TTO/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":"2026-05-29T14:47:40Z","links":{"resolver":"https://pith.science/pith/M6H2BEZM6YM45VVEAIBEGX4TTO","bundle":"https://pith.science/pith/M6H2BEZM6YM45VVEAIBEGX4TTO/bundle.json","state":"https://pith.science/pith/M6H2BEZM6YM45VVEAIBEGX4TTO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6H2BEZM6YM45VVEAIBEGX4TTO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:M6H2BEZM6YM45VVEAIBEGX4TTO","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":"e7ffa80bb60802d693410fd8aeabc3c02b54e5094aee2e63c20087de26dc2100","cross_cats_sorted":["math-ph","math.DG","math.FA","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-09-23T19:54:33Z","title_canon_sha256":"8de59af7b54b5d899bda5e60853ea9a6c2893ba6a214de9aa76d2c58dc2fbc71"},"schema_version":"1.0","source":{"id":"1309.5937","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5937","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5937v2","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5937","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"M6H2BEZM6YM4","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"M6H2BEZM6YM45VVE","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"M6H2BEZM","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:f5c648b281e1cd74b0a7edb9c456371ab939ab3b2d60633cd105b8ad470e8a94","target":"graph","created_at":"2026-05-18T00:12:11Z","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 article deals with intrinsic metrics, Dirac operators and spectral triples induced by regular Dirichlet and resistance forms. We show, in particular, that if a local resistance form is given and the space is compact in resistance metric, then the intrinsic metric yields a geodesic space. Given a regular Dirichlet form, we consider Dirac operators within the framework of differential 1-forms proposed by Cipriani and Sauvageot, and comment on its spectral properties. If the Dirichlet form admits a carr\\'e operator and the generator has discrete spectrum, then we can construct a related spect","authors_text":"Alexander Teplyaev, Daniel J. Kelleher, Michael Hinz","cross_cats":["math-ph","math.DG","math.FA","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-09-23T19:54:33Z","title":"Metrics and spectral triples for Dirichlet and resistance forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5937","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":"sha256:3166e4179d8a19356d9331a0ec93d98278ea89e3b4cf2ee1ef1a7611e298350c","target":"record","created_at":"2026-05-18T00:12:11Z","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":"e7ffa80bb60802d693410fd8aeabc3c02b54e5094aee2e63c20087de26dc2100","cross_cats_sorted":["math-ph","math.DG","math.FA","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-09-23T19:54:33Z","title_canon_sha256":"8de59af7b54b5d899bda5e60853ea9a6c2893ba6a214de9aa76d2c58dc2fbc71"},"schema_version":"1.0","source":{"id":"1309.5937","kind":"arxiv","version":2}},"canonical_sha256":"678fa0932cf619ced6a40202435f939b9b9aac92f51aa646a6f6c6ffcc73fb29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"678fa0932cf619ced6a40202435f939b9b9aac92f51aa646a6f6c6ffcc73fb29","first_computed_at":"2026-05-18T00:12:11.802713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:11.802713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VuVEWqb245CD//lQsTheRN+uUk3ugTIT4LGmWhF7ZuQZKg8o61T5WyzM236A8pYYkj/1oyIUzUTycrVR1DhGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:11.803368Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5937","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3166e4179d8a19356d9331a0ec93d98278ea89e3b4cf2ee1ef1a7611e298350c","sha256:f5c648b281e1cd74b0a7edb9c456371ab939ab3b2d60633cd105b8ad470e8a94"],"state_sha256":"ee8c415968689af3502a9ebd03f7edf24480fa1a894c2afd512f92b198768c12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TwbOIrIuwyXXsR097OiS0GQ2iKuQpizGqt1uutwstnQi6x9BALmlLYec4FwYO+SidYWn0WfApZMDF5oyqLLWDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T14:47:40.816789Z","bundle_sha256":"bf238ebf8f1b0ff43bf6991db9656ec98f5da4c6da30ee4a1530eac01d6fe294"}}