{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4CSW6PRKWF7ZLKIXF4UB32NIAM","short_pith_number":"pith:4CSW6PRK","canonical_record":{"source":{"id":"1309.1305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-05T10:39:41Z","cross_cats_sorted":[],"title_canon_sha256":"60de76da3badf89c960314a194fdebb04feb0a42f85b9dc0fd36a5abe4073f24","abstract_canon_sha256":"cc65e79ec291cbdc221b0ee07082c99db693e092b538b5b0216d2a100291311c"},"schema_version":"1.0"},"canonical_sha256":"e0a56f3e2ab17f95a9172f281de9a8032475ad66eac6a7d3e542104ee95e484c","source":{"kind":"arxiv","id":"1309.1305","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1305","created_at":"2026-05-18T01:00:10Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1305v2","created_at":"2026-05-18T01:00:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1305","created_at":"2026-05-18T01:00:10Z"},{"alias_kind":"pith_short_12","alias_value":"4CSW6PRKWF7Z","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"4CSW6PRKWF7ZLKIX","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"4CSW6PRK","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4CSW6PRKWF7ZLKIXF4UB32NIAM","target":"record","payload":{"canonical_record":{"source":{"id":"1309.1305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-05T10:39:41Z","cross_cats_sorted":[],"title_canon_sha256":"60de76da3badf89c960314a194fdebb04feb0a42f85b9dc0fd36a5abe4073f24","abstract_canon_sha256":"cc65e79ec291cbdc221b0ee07082c99db693e092b538b5b0216d2a100291311c"},"schema_version":"1.0"},"canonical_sha256":"e0a56f3e2ab17f95a9172f281de9a8032475ad66eac6a7d3e542104ee95e484c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:10.571810Z","signature_b64":"qm+9FB5mBIB0wiEXE64TFNREZt4arMeGmqH2bSixqXPpefCVPYDUyTqNvzW+aJjQhmuy/ZpNmFBZ8M4QTrE6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0a56f3e2ab17f95a9172f281de9a8032475ad66eac6a7d3e542104ee95e484c","last_reissued_at":"2026-05-18T01:00:10.571122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:10.571122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.1305","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":"2026-05-18T01:00:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/aT326j5ShgWOkJDeW6V8sZ/bnT8riVMpf8VKZ+ZPqj8X70c/rYyvnAkZkbw+HOCVp5TvVAQZ1fyvmM2ajG0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:41:20.210914Z"},"content_sha256":"d427455d662ef3ab581ff282f9151bffc17db19f5129fccf757aeee0ca1407a9","schema_version":"1.0","event_id":"sha256:d427455d662ef3ab581ff282f9151bffc17db19f5129fccf757aeee0ca1407a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4CSW6PRKWF7ZLKIXF4UB32NIAM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Berman-Konsowa principle for reversible Markov jump processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"F. den Hollander, S. Jansen","submitted_at":"2013-09-05T10:39:41Z","abstract_excerpt":"In this paper we prove a version of the Berman-Konsowa principle for reversible Markov jump processes on Polish spaces. The Berman-Konsowa principle provides a variational formula for the capacity of a pair of disjoint measurable sets. There are two versions, one involving a class of probability measures for random finite paths from one set to the other, the other involving a class of finite unit flows from one set to the other. The Berman-Konsowa principle complements the Dirichlet principle and the Thomson principle, and turns out to be especially useful for obtaining sharp estimates on cros"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1305","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":"2026-05-18T01:00:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"czdFV1qTAALQ/7v96EFHJgN1t4mSvGoPGUPP7sssabrS7EP2MUI9mlv2FT/+xw0dpqbMhF93IeZtBrMqpBf9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:41:20.211659Z"},"content_sha256":"1160bcf791e603c3054fb496095decb958983346276f1973cf54b15b32a1948c","schema_version":"1.0","event_id":"sha256:1160bcf791e603c3054fb496095decb958983346276f1973cf54b15b32a1948c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4CSW6PRKWF7ZLKIXF4UB32NIAM/bundle.json","state_url":"https://pith.science/pith/4CSW6PRKWF7ZLKIXF4UB32NIAM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4CSW6PRKWF7ZLKIXF4UB32NIAM/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":"2026-05-31T14:41:20Z","links":{"resolver":"https://pith.science/pith/4CSW6PRKWF7ZLKIXF4UB32NIAM","bundle":"https://pith.science/pith/4CSW6PRKWF7ZLKIXF4UB32NIAM/bundle.json","state":"https://pith.science/pith/4CSW6PRKWF7ZLKIXF4UB32NIAM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4CSW6PRKWF7ZLKIXF4UB32NIAM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4CSW6PRKWF7ZLKIXF4UB32NIAM","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":"cc65e79ec291cbdc221b0ee07082c99db693e092b538b5b0216d2a100291311c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-05T10:39:41Z","title_canon_sha256":"60de76da3badf89c960314a194fdebb04feb0a42f85b9dc0fd36a5abe4073f24"},"schema_version":"1.0","source":{"id":"1309.1305","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1305","created_at":"2026-05-18T01:00:10Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1305v2","created_at":"2026-05-18T01:00:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1305","created_at":"2026-05-18T01:00:10Z"},{"alias_kind":"pith_short_12","alias_value":"4CSW6PRKWF7Z","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"4CSW6PRKWF7ZLKIX","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"4CSW6PRK","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:1160bcf791e603c3054fb496095decb958983346276f1973cf54b15b32a1948c","target":"graph","created_at":"2026-05-18T01:00:10Z","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":"In this paper we prove a version of the Berman-Konsowa principle for reversible Markov jump processes on Polish spaces. The Berman-Konsowa principle provides a variational formula for the capacity of a pair of disjoint measurable sets. There are two versions, one involving a class of probability measures for random finite paths from one set to the other, the other involving a class of finite unit flows from one set to the other. The Berman-Konsowa principle complements the Dirichlet principle and the Thomson principle, and turns out to be especially useful for obtaining sharp estimates on cros","authors_text":"F. den Hollander, S. Jansen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-05T10:39:41Z","title":"Berman-Konsowa principle for reversible Markov jump processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1305","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:d427455d662ef3ab581ff282f9151bffc17db19f5129fccf757aeee0ca1407a9","target":"record","created_at":"2026-05-18T01:00:10Z","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":"cc65e79ec291cbdc221b0ee07082c99db693e092b538b5b0216d2a100291311c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-05T10:39:41Z","title_canon_sha256":"60de76da3badf89c960314a194fdebb04feb0a42f85b9dc0fd36a5abe4073f24"},"schema_version":"1.0","source":{"id":"1309.1305","kind":"arxiv","version":2}},"canonical_sha256":"e0a56f3e2ab17f95a9172f281de9a8032475ad66eac6a7d3e542104ee95e484c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0a56f3e2ab17f95a9172f281de9a8032475ad66eac6a7d3e542104ee95e484c","first_computed_at":"2026-05-18T01:00:10.571122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:10.571122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qm+9FB5mBIB0wiEXE64TFNREZt4arMeGmqH2bSixqXPpefCVPYDUyTqNvzW+aJjQhmuy/ZpNmFBZ8M4QTrE6Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:10.571810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1305","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d427455d662ef3ab581ff282f9151bffc17db19f5129fccf757aeee0ca1407a9","sha256:1160bcf791e603c3054fb496095decb958983346276f1973cf54b15b32a1948c"],"state_sha256":"da89226f668f9857c6ccd3f1b6f62028565e09b7bc30b8d97bcea7a202dd1be7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cM6EBg+o/LLye9R1VSVvH76ktVeO+RjVB3J81klDjf6ULMlZt+br/mGWwnwz6tVgGVooq+SksUnrriMpc6K6Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:41:20.215618Z","bundle_sha256":"5e61851efc7729dfdad38cfbfd6ed813242d6c79b6c4d50db86919c64f41122d"}}