{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4KYRGUGRTZDNBDZ6OXAKOVDNDZ","short_pith_number":"pith:4KYRGUGR","canonical_record":{"source":{"id":"1402.0298","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-03T07:39:16Z","cross_cats_sorted":[],"title_canon_sha256":"201094fe1d1d9a456d3adcf9416b3af983381d75bb57d7681cce5d227647101d","abstract_canon_sha256":"a06e980ce69d80af6d2f02195413517c17b84a137ca93a92cdb6f6372ef36d5e"},"schema_version":"1.0"},"canonical_sha256":"e2b11350d19e46d08f3e75c0a7546d1e78a6497a55ef3b364c3a454c09c6b6a5","source":{"kind":"arxiv","id":"1402.0298","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0298","created_at":"2026-07-05T01:17:36Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0298v7","created_at":"2026-07-05T01:17:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0298","created_at":"2026-07-05T01:17:36Z"},{"alias_kind":"pith_short_12","alias_value":"4KYRGUGRTZDN","created_at":"2026-07-05T01:17:36Z"},{"alias_kind":"pith_short_16","alias_value":"4KYRGUGRTZDNBDZ6","created_at":"2026-07-05T01:17:36Z"},{"alias_kind":"pith_short_8","alias_value":"4KYRGUGR","created_at":"2026-07-05T01:17:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4KYRGUGRTZDNBDZ6OXAKOVDNDZ","target":"record","payload":{"canonical_record":{"source":{"id":"1402.0298","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-03T07:39:16Z","cross_cats_sorted":[],"title_canon_sha256":"201094fe1d1d9a456d3adcf9416b3af983381d75bb57d7681cce5d227647101d","abstract_canon_sha256":"a06e980ce69d80af6d2f02195413517c17b84a137ca93a92cdb6f6372ef36d5e"},"schema_version":"1.0"},"canonical_sha256":"e2b11350d19e46d08f3e75c0a7546d1e78a6497a55ef3b364c3a454c09c6b6a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:17:36.320276Z","signature_b64":"pwDT39f3XJJEi0HUn1M5uzYBQsH7TCh0mkJpkb5vXU7VAAORdgLcuEt7d4QpLNSd24tYAZxM6Ptm4sS1Q+M6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2b11350d19e46d08f3e75c0a7546d1e78a6497a55ef3b364c3a454c09c6b6a5","last_reissued_at":"2026-07-05T01:17:36.319847Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:17:36.319847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.0298","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:17:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"92x6hBdHCqBuAPhaVdGrfY3n57p8nHuX9nKI0XXGg0wEIMLaijSYEXqAZrlLaKImSoDgCUZN/RsLj6eliqPZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T21:05:48.744649Z"},"content_sha256":"793e24ba2b33ec06d05c2b5b752d11625382af11f03a8faacb1fc256046284fb","schema_version":"1.0","event_id":"sha256:793e24ba2b33ec06d05c2b5b752d11625382af11f03a8faacb1fc256046284fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4KYRGUGRTZDNBDZ6OXAKOVDNDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From loop clusters and random interlacement to the free field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Titus Lupu (LM-Orsay)","submitted_at":"2014-02-03T07:39:16Z","abstract_excerpt":"It was shown by Le Jan that the occupation field of a Poisson ensemble of Markov loops (\"loop soup\") of parameter one-half associated to a transient symmetric Markov jump process on a network is half the square of the Gaussian free field on this network. We construct a coupling between these loops and the free field such that an additional constraint holds: the sign of the free field is constant on each cluster of loops. As a consequence of our coupling we deduce that the loop clusters of parameter one-half do not percolate on periodic lattices. We also construct a coupling between the random "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0298","kind":"arxiv","version":7},"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/1402.0298/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":"2026-07-05T01:17:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WcctsNkrxmF0eBiHT7/IDDyx3Z9u3adOFn1zDcpiAUM+/3Ypv1CGYFUH68VOG0TUQShr4BssIbxfzzugs33KCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T21:05:48.745051Z"},"content_sha256":"11d62bc37afe6b6d2248f1699f67f9e72b429020f22dbae3cb49f6a30d94efc5","schema_version":"1.0","event_id":"sha256:11d62bc37afe6b6d2248f1699f67f9e72b429020f22dbae3cb49f6a30d94efc5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4KYRGUGRTZDNBDZ6OXAKOVDNDZ/bundle.json","state_url":"https://pith.science/pith/4KYRGUGRTZDNBDZ6OXAKOVDNDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4KYRGUGRTZDNBDZ6OXAKOVDNDZ/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":"2026-08-17T21:05:48Z","links":{"resolver":"https://pith.science/pith/4KYRGUGRTZDNBDZ6OXAKOVDNDZ","bundle":"https://pith.science/pith/4KYRGUGRTZDNBDZ6OXAKOVDNDZ/bundle.json","state":"https://pith.science/pith/4KYRGUGRTZDNBDZ6OXAKOVDNDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4KYRGUGRTZDNBDZ6OXAKOVDNDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4KYRGUGRTZDNBDZ6OXAKOVDNDZ","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":"a06e980ce69d80af6d2f02195413517c17b84a137ca93a92cdb6f6372ef36d5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-03T07:39:16Z","title_canon_sha256":"201094fe1d1d9a456d3adcf9416b3af983381d75bb57d7681cce5d227647101d"},"schema_version":"1.0","source":{"id":"1402.0298","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0298","created_at":"2026-07-05T01:17:36Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0298v7","created_at":"2026-07-05T01:17:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0298","created_at":"2026-07-05T01:17:36Z"},{"alias_kind":"pith_short_12","alias_value":"4KYRGUGRTZDN","created_at":"2026-07-05T01:17:36Z"},{"alias_kind":"pith_short_16","alias_value":"4KYRGUGRTZDNBDZ6","created_at":"2026-07-05T01:17:36Z"},{"alias_kind":"pith_short_8","alias_value":"4KYRGUGR","created_at":"2026-07-05T01:17:36Z"}],"graph_snapshots":[{"event_id":"sha256:11d62bc37afe6b6d2248f1699f67f9e72b429020f22dbae3cb49f6a30d94efc5","target":"graph","created_at":"2026-07-05T01:17:36Z","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/1402.0298/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It was shown by Le Jan that the occupation field of a Poisson ensemble of Markov loops (\"loop soup\") of parameter one-half associated to a transient symmetric Markov jump process on a network is half the square of the Gaussian free field on this network. We construct a coupling between these loops and the free field such that an additional constraint holds: the sign of the free field is constant on each cluster of loops. As a consequence of our coupling we deduce that the loop clusters of parameter one-half do not percolate on periodic lattices. We also construct a coupling between the random ","authors_text":"Titus Lupu (LM-Orsay)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-03T07:39:16Z","title":"From loop clusters and random interlacement to the free field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0298","kind":"arxiv","version":7},"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":"sha256:793e24ba2b33ec06d05c2b5b752d11625382af11f03a8faacb1fc256046284fb","target":"record","created_at":"2026-07-05T01:17:36Z","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":"a06e980ce69d80af6d2f02195413517c17b84a137ca93a92cdb6f6372ef36d5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-03T07:39:16Z","title_canon_sha256":"201094fe1d1d9a456d3adcf9416b3af983381d75bb57d7681cce5d227647101d"},"schema_version":"1.0","source":{"id":"1402.0298","kind":"arxiv","version":7}},"canonical_sha256":"e2b11350d19e46d08f3e75c0a7546d1e78a6497a55ef3b364c3a454c09c6b6a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2b11350d19e46d08f3e75c0a7546d1e78a6497a55ef3b364c3a454c09c6b6a5","first_computed_at":"2026-07-05T01:17:36.319847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:17:36.319847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pwDT39f3XJJEi0HUn1M5uzYBQsH7TCh0mkJpkb5vXU7VAAORdgLcuEt7d4QpLNSd24tYAZxM6Ptm4sS1Q+M6DA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:17:36.320276Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0298","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:793e24ba2b33ec06d05c2b5b752d11625382af11f03a8faacb1fc256046284fb","sha256:11d62bc37afe6b6d2248f1699f67f9e72b429020f22dbae3cb49f6a30d94efc5"],"state_sha256":"37e9cd8d7b867da680a48ab376f6d6577e18c0203345aee843dff7ecd02dd4a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5uljQkg3UznvplLsSvRi0BLjn0+YSt0oYa8r9ErO2QzEwNoOp0+jARzipX34SJMH+HN9jwaeIIaJQYY1LBs4Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T21:05:48.747493Z","bundle_sha256":"ab11a60a950d498e824d578f2953bbc1cb2d2f3311042905a2ca27a46ebc0bee"}}