{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6LPETR5Q5M3WXCDA6HJPFHUF2A","short_pith_number":"pith:6LPETR5Q","canonical_record":{"source":{"id":"1501.01100","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-06T07:35:05Z","cross_cats_sorted":["math.AP","math.FA","math.MP"],"title_canon_sha256":"89ac5604288b3a28948222b41ca5925eadcd9b3bf0a34b382041a1e940a8c4b0","abstract_canon_sha256":"f425335ff5f5df3714e2e83d51682377443b20bfc1bf867b9f4b51df20df2682"},"schema_version":"1.0"},"canonical_sha256":"f2de49c7b0eb376b8860f1d2f29e85d020715d85a69349f11efa333aebbf86d8","source":{"kind":"arxiv","id":"1501.01100","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01100","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01100v3","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01100","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"pith_short_12","alias_value":"6LPETR5Q5M3W","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6LPETR5Q5M3WXCDA","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6LPETR5Q","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6LPETR5Q5M3WXCDA6HJPFHUF2A","target":"record","payload":{"canonical_record":{"source":{"id":"1501.01100","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-06T07:35:05Z","cross_cats_sorted":["math.AP","math.FA","math.MP"],"title_canon_sha256":"89ac5604288b3a28948222b41ca5925eadcd9b3bf0a34b382041a1e940a8c4b0","abstract_canon_sha256":"f425335ff5f5df3714e2e83d51682377443b20bfc1bf867b9f4b51df20df2682"},"schema_version":"1.0"},"canonical_sha256":"f2de49c7b0eb376b8860f1d2f29e85d020715d85a69349f11efa333aebbf86d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:41.171688Z","signature_b64":"GmdUfEHV5S+ytW7JEnABbst2mvwDp5NXl0KMAECVOxKm5kA4PIFjK3UtTaN/c5TkDnw0w9YG5HvjQMzr9iQxCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2de49c7b0eb376b8860f1d2f29e85d020715d85a69349f11efa333aebbf86d8","last_reissued_at":"2026-05-18T01:06:41.171046Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:41.171046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.01100","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9bRKGqNnBZ0dXLNmNMXqLjz8dBXQi++FWanDrsNrEUDG9uYn7XHy1LOynByaz4/ZDI0X2pgTK89USlrfS35cAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T09:49:35.788544Z"},"content_sha256":"e98e2cefeb23ff37eb7d646b585150fd9c1c0e1e3eee3ca14d7ebee84f6b2aec","schema_version":"1.0","event_id":"sha256:e98e2cefeb23ff37eb7d646b585150fd9c1c0e1e3eee3ca14d7ebee84f6b2aec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6LPETR5Q5M3WXCDA6HJPFHUF2A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Magnetic fields on resistance spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Luke Rogers, Michael Hinz","submitted_at":"2015-01-06T07:35:05Z","abstract_excerpt":"On a metric measure space $X$ that supports a regular, strongly local resistance form we consider a magnetic energy form that corresponds to the magnetic Laplacian for a particle confined to $X$. We provide sufficient conditions for closability and self-adjointness in terms of geometric conditions on the reference measure without assuming energy dominance."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01100","kind":"arxiv","version":3},"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":"2026-05-18T01:06:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yxQAzaduXeIQhrLuBnoujepZmRCifrOvs4x8GjEmuicnUhbSV+aAaIWpW0AYjEgzN4nkRDS4ZIXS/m1mSb/ABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T09:49:35.788892Z"},"content_sha256":"07c7b8cd45ef333b80ab3161743aff09df5743f8453fbfe0f5a0919d456c1d3c","schema_version":"1.0","event_id":"sha256:07c7b8cd45ef333b80ab3161743aff09df5743f8453fbfe0f5a0919d456c1d3c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LPETR5Q5M3WXCDA6HJPFHUF2A/bundle.json","state_url":"https://pith.science/pith/6LPETR5Q5M3WXCDA6HJPFHUF2A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LPETR5Q5M3WXCDA6HJPFHUF2A/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":"2026-06-02T09:49:35Z","links":{"resolver":"https://pith.science/pith/6LPETR5Q5M3WXCDA6HJPFHUF2A","bundle":"https://pith.science/pith/6LPETR5Q5M3WXCDA6HJPFHUF2A/bundle.json","state":"https://pith.science/pith/6LPETR5Q5M3WXCDA6HJPFHUF2A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LPETR5Q5M3WXCDA6HJPFHUF2A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6LPETR5Q5M3WXCDA6HJPFHUF2A","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":"f425335ff5f5df3714e2e83d51682377443b20bfc1bf867b9f4b51df20df2682","cross_cats_sorted":["math.AP","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-06T07:35:05Z","title_canon_sha256":"89ac5604288b3a28948222b41ca5925eadcd9b3bf0a34b382041a1e940a8c4b0"},"schema_version":"1.0","source":{"id":"1501.01100","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01100","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01100v3","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01100","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"pith_short_12","alias_value":"6LPETR5Q5M3W","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6LPETR5Q5M3WXCDA","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6LPETR5Q","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:07c7b8cd45ef333b80ab3161743aff09df5743f8453fbfe0f5a0919d456c1d3c","target":"graph","created_at":"2026-05-18T01:06:41Z","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":"On a metric measure space $X$ that supports a regular, strongly local resistance form we consider a magnetic energy form that corresponds to the magnetic Laplacian for a particle confined to $X$. We provide sufficient conditions for closability and self-adjointness in terms of geometric conditions on the reference measure without assuming energy dominance.","authors_text":"Luke Rogers, Michael Hinz","cross_cats":["math.AP","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-06T07:35:05Z","title":"Magnetic fields on resistance spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01100","kind":"arxiv","version":3},"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:e98e2cefeb23ff37eb7d646b585150fd9c1c0e1e3eee3ca14d7ebee84f6b2aec","target":"record","created_at":"2026-05-18T01:06:41Z","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":"f425335ff5f5df3714e2e83d51682377443b20bfc1bf867b9f4b51df20df2682","cross_cats_sorted":["math.AP","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-06T07:35:05Z","title_canon_sha256":"89ac5604288b3a28948222b41ca5925eadcd9b3bf0a34b382041a1e940a8c4b0"},"schema_version":"1.0","source":{"id":"1501.01100","kind":"arxiv","version":3}},"canonical_sha256":"f2de49c7b0eb376b8860f1d2f29e85d020715d85a69349f11efa333aebbf86d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2de49c7b0eb376b8860f1d2f29e85d020715d85a69349f11efa333aebbf86d8","first_computed_at":"2026-05-18T01:06:41.171046Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:41.171046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GmdUfEHV5S+ytW7JEnABbst2mvwDp5NXl0KMAECVOxKm5kA4PIFjK3UtTaN/c5TkDnw0w9YG5HvjQMzr9iQxCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:41.171688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01100","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e98e2cefeb23ff37eb7d646b585150fd9c1c0e1e3eee3ca14d7ebee84f6b2aec","sha256:07c7b8cd45ef333b80ab3161743aff09df5743f8453fbfe0f5a0919d456c1d3c"],"state_sha256":"084a06a07ac7ca507151df6e34ceb2bf780a2a36ade723a3355e7f3bc9dbd68c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DMrBfPjhQBIkcXC7p8ixTcW7U1R1fC2qC8mkebx4W+Q9cW7DKhbSFb+SyIJVKSkRnnSXunAlfkZnkt5sZPMXAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T09:49:35.790796Z","bundle_sha256":"c06b76225bb4dd6606a5aff7ab2e2b60177f24bba2c1874f89a712dfa24e68a2"}}