{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HSO6SL7A625KOGSBSDE2GOYWZW","short_pith_number":"pith:HSO6SL7A","canonical_record":{"source":{"id":"1504.07139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-27T15:49:45Z","cross_cats_sorted":[],"title_canon_sha256":"98d6df48abebe1931d7a025bb3dab89cfb16db14d244ef0952b918c573a2aac1","abstract_canon_sha256":"6f9e6b99a2c8b2a67e1267d5c4013f73707a77d05171c773bb4f24fac985dd5b"},"schema_version":"1.0"},"canonical_sha256":"3c9de92fe0f6baa71a4190c9a33b16cda4f2b503a63b603e9f789ae1a35acaa5","source":{"kind":"arxiv","id":"1504.07139","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07139","created_at":"2026-05-18T02:17:43Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07139v1","created_at":"2026-05-18T02:17:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07139","created_at":"2026-05-18T02:17:43Z"},{"alias_kind":"pith_short_12","alias_value":"HSO6SL7A625K","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HSO6SL7A625KOGSB","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HSO6SL7A","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HSO6SL7A625KOGSBSDE2GOYWZW","target":"record","payload":{"canonical_record":{"source":{"id":"1504.07139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-27T15:49:45Z","cross_cats_sorted":[],"title_canon_sha256":"98d6df48abebe1931d7a025bb3dab89cfb16db14d244ef0952b918c573a2aac1","abstract_canon_sha256":"6f9e6b99a2c8b2a67e1267d5c4013f73707a77d05171c773bb4f24fac985dd5b"},"schema_version":"1.0"},"canonical_sha256":"3c9de92fe0f6baa71a4190c9a33b16cda4f2b503a63b603e9f789ae1a35acaa5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:43.616464Z","signature_b64":"7SU8GuRt1b5Itps3NoMd3lc//kwQcNvrT6UI7pRv5kjIIcgFSQeWIdSMjcOF+c0PrKrOF3kJ1fK2cMkSjr4ADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c9de92fe0f6baa71a4190c9a33b16cda4f2b503a63b603e9f789ae1a35acaa5","last_reissued_at":"2026-05-18T02:17:43.616063Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:43.616063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.07139","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":"2026-05-18T02:17:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dB2e8TwX8mAhBKDxSERGANg4fYvUSCFVhj3msOJmQj13Ct3Gz7xFvUJfnPTpo2KfUP94roN3wqvIiwUptuV3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T22:28:29.527922Z"},"content_sha256":"dc744ff0c9b0ca2ba25b22faaf5b0f9eec4279a4afed30ecd5d82248928de7d4","schema_version":"1.0","event_id":"sha256:dc744ff0c9b0ca2ba25b22faaf5b0f9eec4279a4afed30ecd5d82248928de7d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HSO6SL7A625KOGSBSDE2GOYWZW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hammersley's harness process: invariant distributions and height fluctuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Timo Sepp\\\"al\\\"ainen, Yun Zhai","submitted_at":"2015-04-27T15:49:45Z","abstract_excerpt":"We study the invariant distributions of Hammersley's serial harness process in all dimensions and height fluctuations in one dimension. Subject to mild moment assumptions there is essentially one unique invariant distribution, and all other invariant distributions are obtained by adding harmonic functions of the averaging kernel. We identify one Gaussian case where the invariant distribution is i.i.d. Height fluctuations in one dimension obey the stochastic heat equation with additive noise (Edwards-Wilkinson universality). We prove this for correlated initial data subject to polynomial decay "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07139","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":""},"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":"2026-05-18T02:17:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bh7ExFQdkth7CF1Fr4oXAWygHdmKmvGzX1M4P4cjYv7yyfZho8ysOFXEiokO+jo/lysW78WVK/zjncxP99IQAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T22:28:29.528265Z"},"content_sha256":"ae49fdd0556b5de8a6318663e66dc0dd8160d6ed682b191acd31f96b240d3a07","schema_version":"1.0","event_id":"sha256:ae49fdd0556b5de8a6318663e66dc0dd8160d6ed682b191acd31f96b240d3a07"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HSO6SL7A625KOGSBSDE2GOYWZW/bundle.json","state_url":"https://pith.science/pith/HSO6SL7A625KOGSBSDE2GOYWZW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HSO6SL7A625KOGSBSDE2GOYWZW/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":"2026-06-19T22:28:29Z","links":{"resolver":"https://pith.science/pith/HSO6SL7A625KOGSBSDE2GOYWZW","bundle":"https://pith.science/pith/HSO6SL7A625KOGSBSDE2GOYWZW/bundle.json","state":"https://pith.science/pith/HSO6SL7A625KOGSBSDE2GOYWZW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HSO6SL7A625KOGSBSDE2GOYWZW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HSO6SL7A625KOGSBSDE2GOYWZW","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":"6f9e6b99a2c8b2a67e1267d5c4013f73707a77d05171c773bb4f24fac985dd5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-27T15:49:45Z","title_canon_sha256":"98d6df48abebe1931d7a025bb3dab89cfb16db14d244ef0952b918c573a2aac1"},"schema_version":"1.0","source":{"id":"1504.07139","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07139","created_at":"2026-05-18T02:17:43Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07139v1","created_at":"2026-05-18T02:17:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07139","created_at":"2026-05-18T02:17:43Z"},{"alias_kind":"pith_short_12","alias_value":"HSO6SL7A625K","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HSO6SL7A625KOGSB","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HSO6SL7A","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:ae49fdd0556b5de8a6318663e66dc0dd8160d6ed682b191acd31f96b240d3a07","target":"graph","created_at":"2026-05-18T02:17:43Z","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":"We study the invariant distributions of Hammersley's serial harness process in all dimensions and height fluctuations in one dimension. Subject to mild moment assumptions there is essentially one unique invariant distribution, and all other invariant distributions are obtained by adding harmonic functions of the averaging kernel. We identify one Gaussian case where the invariant distribution is i.i.d. Height fluctuations in one dimension obey the stochastic heat equation with additive noise (Edwards-Wilkinson universality). We prove this for correlated initial data subject to polynomial decay ","authors_text":"Timo Sepp\\\"al\\\"ainen, Yun Zhai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-27T15:49:45Z","title":"Hammersley's harness process: invariant distributions and height fluctuations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07139","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:dc744ff0c9b0ca2ba25b22faaf5b0f9eec4279a4afed30ecd5d82248928de7d4","target":"record","created_at":"2026-05-18T02:17:43Z","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":"6f9e6b99a2c8b2a67e1267d5c4013f73707a77d05171c773bb4f24fac985dd5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-27T15:49:45Z","title_canon_sha256":"98d6df48abebe1931d7a025bb3dab89cfb16db14d244ef0952b918c573a2aac1"},"schema_version":"1.0","source":{"id":"1504.07139","kind":"arxiv","version":1}},"canonical_sha256":"3c9de92fe0f6baa71a4190c9a33b16cda4f2b503a63b603e9f789ae1a35acaa5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c9de92fe0f6baa71a4190c9a33b16cda4f2b503a63b603e9f789ae1a35acaa5","first_computed_at":"2026-05-18T02:17:43.616063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:43.616063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7SU8GuRt1b5Itps3NoMd3lc//kwQcNvrT6UI7pRv5kjIIcgFSQeWIdSMjcOF+c0PrKrOF3kJ1fK2cMkSjr4ADg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:43.616464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.07139","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc744ff0c9b0ca2ba25b22faaf5b0f9eec4279a4afed30ecd5d82248928de7d4","sha256:ae49fdd0556b5de8a6318663e66dc0dd8160d6ed682b191acd31f96b240d3a07"],"state_sha256":"a28f0a364848382dabff4d1052ee9b8a8a928a68ad097250b56f098ec0c49890"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SVK0h6y/TN+cmdd5qZIlVvHmiLiXIXSdr02PmpnqWysJFm6jpoU6oFEQQICekhgjryR0rIfaUuL9ZL03G4cOCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-19T22:28:29.530168Z","bundle_sha256":"a7eda90d9de2da21280efa88bd0d24f67eec682bea866481bd53fc80313d0d38"}}