{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ETPPKFWUDD3RTGEKWSPIVO2VAE","short_pith_number":"pith:ETPPKFWU","canonical_record":{"source":{"id":"1806.02469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-07T00:31:08Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"a272f886e58a73b16aca09a60a345aa3470faea46d38098b081130a09d0cdd55","abstract_canon_sha256":"ee0854dd0bd988d33a338f59f51257fb5e5f3040b9c7ecf07751f1bbfb10c380"},"schema_version":"1.0"},"canonical_sha256":"24def516d418f719988ab49e8abb55012485f85be105f24a4c2a836da9f7a448","source":{"kind":"arxiv","id":"1806.02469","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02469","created_at":"2026-05-18T00:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02469v1","created_at":"2026-05-18T00:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02469","created_at":"2026-05-18T00:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"ETPPKFWUDD3R","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ETPPKFWUDD3RTGEK","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ETPPKFWU","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ETPPKFWUDD3RTGEKWSPIVO2VAE","target":"record","payload":{"canonical_record":{"source":{"id":"1806.02469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-07T00:31:08Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"a272f886e58a73b16aca09a60a345aa3470faea46d38098b081130a09d0cdd55","abstract_canon_sha256":"ee0854dd0bd988d33a338f59f51257fb5e5f3040b9c7ecf07751f1bbfb10c380"},"schema_version":"1.0"},"canonical_sha256":"24def516d418f719988ab49e8abb55012485f85be105f24a4c2a836da9f7a448","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:56.744453Z","signature_b64":"Oq8XbMrGFnuVa1j/sI7WHM6i4D+wOg3ELBnUIcRCopQUwlfbM6h9nAkUtV8DjTkGgMPDn/tThvUBj2hGGXp/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24def516d418f719988ab49e8abb55012485f85be105f24a4c2a836da9f7a448","last_reissued_at":"2026-05-18T00:13:56.743686Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:56.743686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.02469","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":"2026-05-18T00:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"214u49T3lGwy686Nk146xxa5AW22pmraAoBslVuFhT5RhoyelnGjz9dRiHSngYpIsk7MyWZjblSpjGCWlxSMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:51:28.203531Z"},"content_sha256":"c3f689ee8db9163c8287d80469a3c3c3ca62eaf13adabc973347d21d5ae0b652","schema_version":"1.0","event_id":"sha256:c3f689ee8db9163c8287d80469a3c3c3ca62eaf13adabc973347d21d5ae0b652"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ETPPKFWUDD3RTGEKWSPIVO2VAE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shape theorem and surface fluctuation for Poisson cylinders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Marcelo Hilario, Petr Panov, Xinyi Li","submitted_at":"2018-06-07T00:31:08Z","abstract_excerpt":"In this work, we prove a shape theorem for Poisson cylinders and give a power law bound on surface fluctuations. We prove that for any $a \\in (1/2, 1)$, conditioned on the origin being in the set of cylinders, every point in this set, whose Euclidean norm is less than $R$, lies at an internal distance less than $R+O(R^a)$ from the origin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02469","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":"2026-05-18T00:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ipsGRGNgSDgJ2icGkx6Au9e/JGAI//JWBLEHbnDd4CmHWWEevlt+7FAXrgLkxx+PQvloEW3aEdnXLdTGYuxPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:51:28.204195Z"},"content_sha256":"0d71a1cb2e788542bebd3fd0528e58a8dc423bd164a967388af56cb8ebc0d947","schema_version":"1.0","event_id":"sha256:0d71a1cb2e788542bebd3fd0528e58a8dc423bd164a967388af56cb8ebc0d947"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ETPPKFWUDD3RTGEKWSPIVO2VAE/bundle.json","state_url":"https://pith.science/pith/ETPPKFWUDD3RTGEKWSPIVO2VAE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ETPPKFWUDD3RTGEKWSPIVO2VAE/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":"2026-05-25T14:51:28Z","links":{"resolver":"https://pith.science/pith/ETPPKFWUDD3RTGEKWSPIVO2VAE","bundle":"https://pith.science/pith/ETPPKFWUDD3RTGEKWSPIVO2VAE/bundle.json","state":"https://pith.science/pith/ETPPKFWUDD3RTGEKWSPIVO2VAE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ETPPKFWUDD3RTGEKWSPIVO2VAE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ETPPKFWUDD3RTGEKWSPIVO2VAE","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":"ee0854dd0bd988d33a338f59f51257fb5e5f3040b9c7ecf07751f1bbfb10c380","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-07T00:31:08Z","title_canon_sha256":"a272f886e58a73b16aca09a60a345aa3470faea46d38098b081130a09d0cdd55"},"schema_version":"1.0","source":{"id":"1806.02469","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02469","created_at":"2026-05-18T00:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02469v1","created_at":"2026-05-18T00:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02469","created_at":"2026-05-18T00:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"ETPPKFWUDD3R","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ETPPKFWUDD3RTGEK","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ETPPKFWU","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:0d71a1cb2e788542bebd3fd0528e58a8dc423bd164a967388af56cb8ebc0d947","target":"graph","created_at":"2026-05-18T00:13:56Z","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":"In this work, we prove a shape theorem for Poisson cylinders and give a power law bound on surface fluctuations. We prove that for any $a \\in (1/2, 1)$, conditioned on the origin being in the set of cylinders, every point in this set, whose Euclidean norm is less than $R$, lies at an internal distance less than $R+O(R^a)$ from the origin.","authors_text":"Marcelo Hilario, Petr Panov, Xinyi Li","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-07T00:31:08Z","title":"Shape theorem and surface fluctuation for Poisson cylinders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02469","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:c3f689ee8db9163c8287d80469a3c3c3ca62eaf13adabc973347d21d5ae0b652","target":"record","created_at":"2026-05-18T00:13:56Z","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":"ee0854dd0bd988d33a338f59f51257fb5e5f3040b9c7ecf07751f1bbfb10c380","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-07T00:31:08Z","title_canon_sha256":"a272f886e58a73b16aca09a60a345aa3470faea46d38098b081130a09d0cdd55"},"schema_version":"1.0","source":{"id":"1806.02469","kind":"arxiv","version":1}},"canonical_sha256":"24def516d418f719988ab49e8abb55012485f85be105f24a4c2a836da9f7a448","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24def516d418f719988ab49e8abb55012485f85be105f24a4c2a836da9f7a448","first_computed_at":"2026-05-18T00:13:56.743686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:56.743686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Oq8XbMrGFnuVa1j/sI7WHM6i4D+wOg3ELBnUIcRCopQUwlfbM6h9nAkUtV8DjTkGgMPDn/tThvUBj2hGGXp/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:56.744453Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.02469","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3f689ee8db9163c8287d80469a3c3c3ca62eaf13adabc973347d21d5ae0b652","sha256:0d71a1cb2e788542bebd3fd0528e58a8dc423bd164a967388af56cb8ebc0d947"],"state_sha256":"25b80ddc3186e1ceb9f55338e12fa8e389bb09d1d8e2cf5a0d8e856b79cbee76"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YtXUjfr4bL7V3j/WuWMjq/N36J/uQTBwVr7tYPxAkqDWdrMp/aHfgxDHypPfj7a0oVZdIwZEQCVWmjwp22pFDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T14:51:28.208173Z","bundle_sha256":"02daf26db77bd58290803f1f701c82907e1aa85013b54248a24efd212bd814d6"}}