{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:RZDJROCLAP2EG4JTSRUQD3YRHD","short_pith_number":"pith:RZDJROCL","canonical_record":{"source":{"id":"1810.04011","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-09T14:12:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"dd5a5cf3ccd66b2ced5e0d10f32782b53ced0d4bcc1a946485d28f28bec98d93","abstract_canon_sha256":"fb890446e609d14f91c4a0b61c927e865ccbb57574fc8fb7b68a8c91f1bca674"},"schema_version":"1.0"},"canonical_sha256":"8e4698b84b03f4437133946901ef1138e4559a5605350f276bb26263815c7ce7","source":{"kind":"arxiv","id":"1810.04011","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04011","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04011v2","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04011","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"RZDJROCLAP2E","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RZDJROCLAP2EG4JT","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RZDJROCL","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:RZDJROCLAP2EG4JTSRUQD3YRHD","target":"record","payload":{"canonical_record":{"source":{"id":"1810.04011","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-09T14:12:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"dd5a5cf3ccd66b2ced5e0d10f32782b53ced0d4bcc1a946485d28f28bec98d93","abstract_canon_sha256":"fb890446e609d14f91c4a0b61c927e865ccbb57574fc8fb7b68a8c91f1bca674"},"schema_version":"1.0"},"canonical_sha256":"8e4698b84b03f4437133946901ef1138e4559a5605350f276bb26263815c7ce7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:04.398095Z","signature_b64":"hjQRgaufZEpeqL1GoURqO6szJ9oKhqRuA0ZsLa2PR+QrH4my8+j3EbHHlqga7iwK2ZuP7DcWgRO31o0Ko30sDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e4698b84b03f4437133946901ef1138e4559a5605350f276bb26263815c7ce7","last_reissued_at":"2026-05-17T23:45:04.397580Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:04.397580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.04011","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":"2026-05-17T23:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"101O2MeAae5aaKrVoFwnBI6qs2yvuy2KlBRgN9LMeFH7pnQdUiBcZNg/SI/LuhDZJCxQcunroBNXeS2Nz5S/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:07:02.569732Z"},"content_sha256":"6998a2deb8c0f9f0ec8854a1c1a1a2d7ba19697e235e6da6c9fe5fca085aface","schema_version":"1.0","event_id":"sha256:6998a2deb8c0f9f0ec8854a1c1a1a2d7ba19697e235e6da6c9fe5fca085aface"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:RZDJROCLAP2EG4JTSRUQD3YRHD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spatial moments for high-dimensional critical contact process, oriented percolation and lattice trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Akira Sakai, Gordon Slade","submitted_at":"2018-10-09T14:12:04Z","abstract_excerpt":"Recently, Holmes and Perkins identified conditions which ensure that for a class of critical lattice models the scaling limit of the range is the range of super-Brownian motion. One of their conditions is an estimate on a spatial moment of order higher than four, which they verified for the sixth moment for spread-out lattice trees in dimensions $d>8$. Chen and Sakai have proved the required moment estimate for spread-out critical oriented percolation in dimensions $d+1>4+1$. We prove estimates on all moments for the spread-out critical contact process in dimensions $d>4$, which in particular "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04011","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":"2026-05-17T23:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RBFVxHPr9aWaaQtgnP7ktl7ZlgQUR+mafQLyfGOoRc1uxvJ5tFscqO6X0fjHkNip+BTM2e3kGzMWdWZlSmBEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:07:02.570067Z"},"content_sha256":"3f9e8c236a42e58129b40c52920d029c743b5722a59683ad29bcc554e3e9e66c","schema_version":"1.0","event_id":"sha256:3f9e8c236a42e58129b40c52920d029c743b5722a59683ad29bcc554e3e9e66c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RZDJROCLAP2EG4JTSRUQD3YRHD/bundle.json","state_url":"https://pith.science/pith/RZDJROCLAP2EG4JTSRUQD3YRHD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RZDJROCLAP2EG4JTSRUQD3YRHD/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":"2026-06-03T06:07:02Z","links":{"resolver":"https://pith.science/pith/RZDJROCLAP2EG4JTSRUQD3YRHD","bundle":"https://pith.science/pith/RZDJROCLAP2EG4JTSRUQD3YRHD/bundle.json","state":"https://pith.science/pith/RZDJROCLAP2EG4JTSRUQD3YRHD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RZDJROCLAP2EG4JTSRUQD3YRHD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RZDJROCLAP2EG4JTSRUQD3YRHD","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":"fb890446e609d14f91c4a0b61c927e865ccbb57574fc8fb7b68a8c91f1bca674","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-09T14:12:04Z","title_canon_sha256":"dd5a5cf3ccd66b2ced5e0d10f32782b53ced0d4bcc1a946485d28f28bec98d93"},"schema_version":"1.0","source":{"id":"1810.04011","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04011","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04011v2","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04011","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"RZDJROCLAP2E","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RZDJROCLAP2EG4JT","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RZDJROCL","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:3f9e8c236a42e58129b40c52920d029c743b5722a59683ad29bcc554e3e9e66c","target":"graph","created_at":"2026-05-17T23:45:04Z","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":"Recently, Holmes and Perkins identified conditions which ensure that for a class of critical lattice models the scaling limit of the range is the range of super-Brownian motion. One of their conditions is an estimate on a spatial moment of order higher than four, which they verified for the sixth moment for spread-out lattice trees in dimensions $d>8$. Chen and Sakai have proved the required moment estimate for spread-out critical oriented percolation in dimensions $d+1>4+1$. We prove estimates on all moments for the spread-out critical contact process in dimensions $d>4$, which in particular ","authors_text":"Akira Sakai, Gordon Slade","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-09T14:12:04Z","title":"Spatial moments for high-dimensional critical contact process, oriented percolation and lattice trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04011","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":"sha256:6998a2deb8c0f9f0ec8854a1c1a1a2d7ba19697e235e6da6c9fe5fca085aface","target":"record","created_at":"2026-05-17T23:45:04Z","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":"fb890446e609d14f91c4a0b61c927e865ccbb57574fc8fb7b68a8c91f1bca674","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-09T14:12:04Z","title_canon_sha256":"dd5a5cf3ccd66b2ced5e0d10f32782b53ced0d4bcc1a946485d28f28bec98d93"},"schema_version":"1.0","source":{"id":"1810.04011","kind":"arxiv","version":2}},"canonical_sha256":"8e4698b84b03f4437133946901ef1138e4559a5605350f276bb26263815c7ce7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e4698b84b03f4437133946901ef1138e4559a5605350f276bb26263815c7ce7","first_computed_at":"2026-05-17T23:45:04.397580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:04.397580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hjQRgaufZEpeqL1GoURqO6szJ9oKhqRuA0ZsLa2PR+QrH4my8+j3EbHHlqga7iwK2ZuP7DcWgRO31o0Ko30sDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:04.398095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04011","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6998a2deb8c0f9f0ec8854a1c1a1a2d7ba19697e235e6da6c9fe5fca085aface","sha256:3f9e8c236a42e58129b40c52920d029c743b5722a59683ad29bcc554e3e9e66c"],"state_sha256":"7f92991567be3ec96239991a45e59e89a8b0236b0d86c4b6f9218029792b17ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m8ZlIMEdY3UjbeRZWf4fUcdYgZiPGox2oxpPadcFgeXjyd/mSoIBvqk2uPSjMPfrebMncwvOozY2DxwByVMnCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:07:02.571980Z","bundle_sha256":"3afccb713558d6ee60b5c412c60e736fc16421a845ec53358cdb00aa57f38818"}}