{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YPO5EGWBEIB6NCETA6VVZGBW2V","short_pith_number":"pith:YPO5EGWB","canonical_record":{"source":{"id":"1609.02447","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-08T14:38:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3c7b8fcc740fa917f1979996b91c1fbf4273fde98b4216216db1e42c168a40a5","abstract_canon_sha256":"56fad09b7913a3208ba659a0741b1751361a51389d2599f43056d6eedb12c718"},"schema_version":"1.0"},"canonical_sha256":"c3ddd21ac12203e6889307ab5c9836d5724c4ef0a68ba8e227b4afacac42abce","source":{"kind":"arxiv","id":"1609.02447","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02447","created_at":"2026-05-17T23:40:21Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02447v2","created_at":"2026-05-17T23:40:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02447","created_at":"2026-05-17T23:40:21Z"},{"alias_kind":"pith_short_12","alias_value":"YPO5EGWBEIB6","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YPO5EGWBEIB6NCET","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YPO5EGWB","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YPO5EGWBEIB6NCETA6VVZGBW2V","target":"record","payload":{"canonical_record":{"source":{"id":"1609.02447","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-08T14:38:44Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3c7b8fcc740fa917f1979996b91c1fbf4273fde98b4216216db1e42c168a40a5","abstract_canon_sha256":"56fad09b7913a3208ba659a0741b1751361a51389d2599f43056d6eedb12c718"},"schema_version":"1.0"},"canonical_sha256":"c3ddd21ac12203e6889307ab5c9836d5724c4ef0a68ba8e227b4afacac42abce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:21.114104Z","signature_b64":"hnKeZP+430w70Oq+I+gc91C8JMfkqBoBe1J+VNpVfUFtkflNZalwV1Uzr2pdeefId70O48Prju7/oHY2cDjRDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3ddd21ac12203e6889307ab5c9836d5724c4ef0a68ba8e227b4afacac42abce","last_reissued_at":"2026-05-17T23:40:21.113336Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:21.113336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.02447","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":"2026-05-17T23:40:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lJGPofssX3LUgijquYfyBswRFRjGaLbnCvehwW/hZuABE/Ze3nPHuJfliDgKlFXK4Ws1EXXS/g3tid7nSCQ1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:34:27.699817Z"},"content_sha256":"eee451440a5553156fdb930f58a237a5484be5eeb71eb2eb67c089651754269f","schema_version":"1.0","event_id":"sha256:eee451440a5553156fdb930f58a237a5484be5eeb71eb2eb67c089651754269f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YPO5EGWBEIB6NCETA6VVZGBW2V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random coalescing geodesics in first-passage percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Christopher Hoffman, Daniel Ahlberg","submitted_at":"2016-09-08T14:38:44Z","abstract_excerpt":"We continue the study of infinite geodesics in planar first-passage percolation, pioneered by Newman in the mid 1990s. Building on more recent work of Hoffman, and Damron and Hanson, we develop an ergodic theory for infinite geodesics via the study of what we shall call `random coalescing geodesics'. Random coalescing geodesics have a range of nice asymptotic properties, such as asymptotic directions and linear Busemann functions. We show that random coalescing geodesics are (in some sense) dense in the space of geodesics. This allows us to extrapolate properties from random coalescing geodesi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02447","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":"2026-05-17T23:40:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GmkLxArC2858pWsjaR89ve5441IO/YM9KqokqP/670ZFoO9KCddAo9qJJBjzbZOzIVTWAVdjPk1P9RDNkfzfAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:34:27.700168Z"},"content_sha256":"4a6e6977d6afa885572f672b31b10159c28bf39b2a5a586d0e0db87ac1b14e2d","schema_version":"1.0","event_id":"sha256:4a6e6977d6afa885572f672b31b10159c28bf39b2a5a586d0e0db87ac1b14e2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YPO5EGWBEIB6NCETA6VVZGBW2V/bundle.json","state_url":"https://pith.science/pith/YPO5EGWBEIB6NCETA6VVZGBW2V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YPO5EGWBEIB6NCETA6VVZGBW2V/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":"2026-06-01T16:34:27Z","links":{"resolver":"https://pith.science/pith/YPO5EGWBEIB6NCETA6VVZGBW2V","bundle":"https://pith.science/pith/YPO5EGWBEIB6NCETA6VVZGBW2V/bundle.json","state":"https://pith.science/pith/YPO5EGWBEIB6NCETA6VVZGBW2V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YPO5EGWBEIB6NCETA6VVZGBW2V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YPO5EGWBEIB6NCETA6VVZGBW2V","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":"56fad09b7913a3208ba659a0741b1751361a51389d2599f43056d6eedb12c718","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-08T14:38:44Z","title_canon_sha256":"3c7b8fcc740fa917f1979996b91c1fbf4273fde98b4216216db1e42c168a40a5"},"schema_version":"1.0","source":{"id":"1609.02447","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02447","created_at":"2026-05-17T23:40:21Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02447v2","created_at":"2026-05-17T23:40:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02447","created_at":"2026-05-17T23:40:21Z"},{"alias_kind":"pith_short_12","alias_value":"YPO5EGWBEIB6","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YPO5EGWBEIB6NCET","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YPO5EGWB","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:4a6e6977d6afa885572f672b31b10159c28bf39b2a5a586d0e0db87ac1b14e2d","target":"graph","created_at":"2026-05-17T23:40:21Z","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 continue the study of infinite geodesics in planar first-passage percolation, pioneered by Newman in the mid 1990s. Building on more recent work of Hoffman, and Damron and Hanson, we develop an ergodic theory for infinite geodesics via the study of what we shall call `random coalescing geodesics'. Random coalescing geodesics have a range of nice asymptotic properties, such as asymptotic directions and linear Busemann functions. We show that random coalescing geodesics are (in some sense) dense in the space of geodesics. This allows us to extrapolate properties from random coalescing geodesi","authors_text":"Christopher Hoffman, Daniel Ahlberg","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-08T14:38:44Z","title":"Random coalescing geodesics in first-passage percolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02447","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:eee451440a5553156fdb930f58a237a5484be5eeb71eb2eb67c089651754269f","target":"record","created_at":"2026-05-17T23:40:21Z","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":"56fad09b7913a3208ba659a0741b1751361a51389d2599f43056d6eedb12c718","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-08T14:38:44Z","title_canon_sha256":"3c7b8fcc740fa917f1979996b91c1fbf4273fde98b4216216db1e42c168a40a5"},"schema_version":"1.0","source":{"id":"1609.02447","kind":"arxiv","version":2}},"canonical_sha256":"c3ddd21ac12203e6889307ab5c9836d5724c4ef0a68ba8e227b4afacac42abce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3ddd21ac12203e6889307ab5c9836d5724c4ef0a68ba8e227b4afacac42abce","first_computed_at":"2026-05-17T23:40:21.113336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:21.113336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hnKeZP+430w70Oq+I+gc91C8JMfkqBoBe1J+VNpVfUFtkflNZalwV1Uzr2pdeefId70O48Prju7/oHY2cDjRDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:21.114104Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.02447","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eee451440a5553156fdb930f58a237a5484be5eeb71eb2eb67c089651754269f","sha256:4a6e6977d6afa885572f672b31b10159c28bf39b2a5a586d0e0db87ac1b14e2d"],"state_sha256":"b2a1e655d282182d69a3dec2637c7715dc4932c45ddd23533cef3f91b67ecf4f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U0H3vwFKgqOP4YAenpcx/T7VTkbmFnOYCu5jNhm2JlF/a3GHtHQp+opvLXQpljjCuYb3OgX/tE/ei9hiGCMjCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:34:27.702808Z","bundle_sha256":"8e59cce7e07d582e09ff103d55d9a22ee0d912f9775ab5af302706c7ee646409"}}