{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NBRWWNPLLOXWE5EUS5TNNORJ53","short_pith_number":"pith:NBRWWNPL","canonical_record":{"source":{"id":"1411.6688","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-25T00:06:53Z","cross_cats_sorted":[],"title_canon_sha256":"86ab22d260e47ec16199d56e6c36fa29896c60bbcbc45125f293759d134fe304","abstract_canon_sha256":"f53ec1d83d95c6a8749e9ccdfd489d78af330e513ddb509070eb645c03ccb07e"},"schema_version":"1.0"},"canonical_sha256":"68636b35eb5baf6274949766d6ba29eec3d9f9ae0b7e00d1a4babd74cd546384","source":{"kind":"arxiv","id":"1411.6688","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6688","created_at":"2026-05-18T02:32:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6688v1","created_at":"2026-05-18T02:32:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6688","created_at":"2026-05-18T02:32:52Z"},{"alias_kind":"pith_short_12","alias_value":"NBRWWNPLLOXW","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NBRWWNPLLOXWE5EU","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NBRWWNPL","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NBRWWNPLLOXWE5EUS5TNNORJ53","target":"record","payload":{"canonical_record":{"source":{"id":"1411.6688","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-25T00:06:53Z","cross_cats_sorted":[],"title_canon_sha256":"86ab22d260e47ec16199d56e6c36fa29896c60bbcbc45125f293759d134fe304","abstract_canon_sha256":"f53ec1d83d95c6a8749e9ccdfd489d78af330e513ddb509070eb645c03ccb07e"},"schema_version":"1.0"},"canonical_sha256":"68636b35eb5baf6274949766d6ba29eec3d9f9ae0b7e00d1a4babd74cd546384","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:52.654259Z","signature_b64":"MwSBSqKzhYGWv9jQkGty9BEKU03yJ87caoZWt/WkOalIXCewRdcKynt97XGMxLcOpK0Dca74IaVU7HYAr38hAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68636b35eb5baf6274949766d6ba29eec3d9f9ae0b7e00d1a4babd74cd546384","last_reissued_at":"2026-05-18T02:32:52.653804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:52.653804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.6688","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":"2026-05-18T02:32:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KpovfN7m+t042T9klv23L0AteTVs2JtxC0XIiqFn8g1/66qqnpWOJl9GATa1zSK1N5p5hPPCqqlyNIqxMFDBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:41:07.883595Z"},"content_sha256":"72cb77470f62a4e2ea41f161f105449052c3b55dbd143b9d7fa55c07a01025dc","schema_version":"1.0","event_id":"sha256:72cb77470f62a4e2ea41f161f105449052c3b55dbd143b9d7fa55c07a01025dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NBRWWNPLLOXWE5EUS5TNNORJ53","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On percolation in Poisson graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cecilia Holmgren, Johan Bj\\\"orklund, Victor Falgas-Ravry","submitted_at":"2014-11-25T00:06:53Z","abstract_excerpt":"Equip each point $x$ of a homogeneous Poisson process $\\mathcal{P}$ on $\\mathbb{R}$ with $D_x$ edge stubs, where the $D_x$ are i.i.d. positive integer-valued random variables with distribution given by $\\mu$. Following the stable multi-matching scheme introduced by Deijfen, H\\\"aggstrom and Holroyd (2012), we pair off edge stubs in a series of rounds to form the edge set of an infinite component $G$ on the vertex set $\\mathcal{P}$. In this note, we answer questions of Deijfen, Holroyd and Peres (2011) and Deijfen, H\\\"aggstr\\\"om and Holroyd (2012) on percolation (the existence of an infinite con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6688","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":"2026-05-18T02:32:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zB/xYUAKt0B3jLWkZyuZ7OmyGGaWkrN7Fd5ZZjlNRIIvSH91nXCHOaI3QVFwpD6EPrhjNzvOBhLCylfPrZ4GBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:41:07.883940Z"},"content_sha256":"6eb9b5b11e71456f17c7d9ac287d77a33240969c5ff059bc6db8e35d7d53329f","schema_version":"1.0","event_id":"sha256:6eb9b5b11e71456f17c7d9ac287d77a33240969c5ff059bc6db8e35d7d53329f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NBRWWNPLLOXWE5EUS5TNNORJ53/bundle.json","state_url":"https://pith.science/pith/NBRWWNPLLOXWE5EUS5TNNORJ53/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NBRWWNPLLOXWE5EUS5TNNORJ53/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":"2026-06-02T21:41:07Z","links":{"resolver":"https://pith.science/pith/NBRWWNPLLOXWE5EUS5TNNORJ53","bundle":"https://pith.science/pith/NBRWWNPLLOXWE5EUS5TNNORJ53/bundle.json","state":"https://pith.science/pith/NBRWWNPLLOXWE5EUS5TNNORJ53/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NBRWWNPLLOXWE5EUS5TNNORJ53/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NBRWWNPLLOXWE5EUS5TNNORJ53","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":"f53ec1d83d95c6a8749e9ccdfd489d78af330e513ddb509070eb645c03ccb07e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-25T00:06:53Z","title_canon_sha256":"86ab22d260e47ec16199d56e6c36fa29896c60bbcbc45125f293759d134fe304"},"schema_version":"1.0","source":{"id":"1411.6688","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6688","created_at":"2026-05-18T02:32:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6688v1","created_at":"2026-05-18T02:32:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6688","created_at":"2026-05-18T02:32:52Z"},{"alias_kind":"pith_short_12","alias_value":"NBRWWNPLLOXW","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NBRWWNPLLOXWE5EU","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NBRWWNPL","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:6eb9b5b11e71456f17c7d9ac287d77a33240969c5ff059bc6db8e35d7d53329f","target":"graph","created_at":"2026-05-18T02:32:52Z","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":"Equip each point $x$ of a homogeneous Poisson process $\\mathcal{P}$ on $\\mathbb{R}$ with $D_x$ edge stubs, where the $D_x$ are i.i.d. positive integer-valued random variables with distribution given by $\\mu$. Following the stable multi-matching scheme introduced by Deijfen, H\\\"aggstrom and Holroyd (2012), we pair off edge stubs in a series of rounds to form the edge set of an infinite component $G$ on the vertex set $\\mathcal{P}$. In this note, we answer questions of Deijfen, Holroyd and Peres (2011) and Deijfen, H\\\"aggstr\\\"om and Holroyd (2012) on percolation (the existence of an infinite con","authors_text":"Cecilia Holmgren, Johan Bj\\\"orklund, Victor Falgas-Ravry","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-25T00:06:53Z","title":"On percolation in Poisson graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6688","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":"sha256:72cb77470f62a4e2ea41f161f105449052c3b55dbd143b9d7fa55c07a01025dc","target":"record","created_at":"2026-05-18T02:32:52Z","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":"f53ec1d83d95c6a8749e9ccdfd489d78af330e513ddb509070eb645c03ccb07e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-25T00:06:53Z","title_canon_sha256":"86ab22d260e47ec16199d56e6c36fa29896c60bbcbc45125f293759d134fe304"},"schema_version":"1.0","source":{"id":"1411.6688","kind":"arxiv","version":1}},"canonical_sha256":"68636b35eb5baf6274949766d6ba29eec3d9f9ae0b7e00d1a4babd74cd546384","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68636b35eb5baf6274949766d6ba29eec3d9f9ae0b7e00d1a4babd74cd546384","first_computed_at":"2026-05-18T02:32:52.653804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:52.653804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MwSBSqKzhYGWv9jQkGty9BEKU03yJ87caoZWt/WkOalIXCewRdcKynt97XGMxLcOpK0Dca74IaVU7HYAr38hAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:52.654259Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6688","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72cb77470f62a4e2ea41f161f105449052c3b55dbd143b9d7fa55c07a01025dc","sha256:6eb9b5b11e71456f17c7d9ac287d77a33240969c5ff059bc6db8e35d7d53329f"],"state_sha256":"e1f5faaf3bd36ed8fc2f35df79afa49b11132c5619a1eabdfda7d16a01d91e5f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YhAchrtbuX7s7VYEVXZ/3MAlZth3hMA+v3b5/C1qqX/paA4EMlp4Q8u+ryw5yHfwf/C1JzDfE71mDmA79RU9Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:41:07.885902Z","bundle_sha256":"12c121d3e8c127a7fa2dd3a00a2b41e0e80f01725c0daad63fe4b4be166850e4"}}