{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:X3TMZOTDDGYLZXLVNJJHHMZDMG","short_pith_number":"pith:X3TMZOTD","canonical_record":{"source":{"id":"1606.03764","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-12T21:29:15Z","cross_cats_sorted":[],"title_canon_sha256":"94c90efafce9fb85d06ec9f2cc48f49df345decf854aefd18df14090c0f4a433","abstract_canon_sha256":"ea5822e0fd7e89f59eef09646cfda993347d301c80d85cad1533b20fdedefe4d"},"schema_version":"1.0"},"canonical_sha256":"bee6ccba6319b0bcdd756a5273b32361a316c75db5e4ae9d8e8bb71f1ac1e25d","source":{"kind":"arxiv","id":"1606.03764","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03764","created_at":"2026-05-18T01:03:18Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03764v1","created_at":"2026-05-18T01:03:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03764","created_at":"2026-05-18T01:03:18Z"},{"alias_kind":"pith_short_12","alias_value":"X3TMZOTDDGYL","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X3TMZOTDDGYLZXLV","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X3TMZOTD","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:X3TMZOTDDGYLZXLVNJJHHMZDMG","target":"record","payload":{"canonical_record":{"source":{"id":"1606.03764","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-12T21:29:15Z","cross_cats_sorted":[],"title_canon_sha256":"94c90efafce9fb85d06ec9f2cc48f49df345decf854aefd18df14090c0f4a433","abstract_canon_sha256":"ea5822e0fd7e89f59eef09646cfda993347d301c80d85cad1533b20fdedefe4d"},"schema_version":"1.0"},"canonical_sha256":"bee6ccba6319b0bcdd756a5273b32361a316c75db5e4ae9d8e8bb71f1ac1e25d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:18.629552Z","signature_b64":"V9MQj9aY+PdlMvOW5bLQ35yDbYoTyC7osY3WWHmEBvbnRc1XylssL+wVavyd50VQQtUL3CRMeDdUjRoFVNjVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bee6ccba6319b0bcdd756a5273b32361a316c75db5e4ae9d8e8bb71f1ac1e25d","last_reissued_at":"2026-05-18T01:03:18.629062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:18.629062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.03764","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":"2026-05-18T01:03:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IVIA6wurfty2uzPAmkT4lzjyd4k8jWxdb+Fd1unQCSPe6a03jfoOU97XWSR0Pdxu/G0x5GstnWjq39ZMWzkNCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:51:50.596487Z"},"content_sha256":"a8bcccf09c18471a871b70edfd4db417421ffdd9de1791fe68840ecd027c1143","schema_version":"1.0","event_id":"sha256:a8bcccf09c18471a871b70edfd4db417421ffdd9de1791fe68840ecd027c1143"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:X3TMZOTDDGYLZXLVNJJHHMZDMG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Percolation on trees as a Brownian excursion: from Gaussian to Kolmogorov-Smirnov to Exponential statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Francesc Font-Clos, Nicholas R. Moloney","submitted_at":"2016-06-12T21:29:15Z","abstract_excerpt":"We calculate the distribution of the size of the percolating cluster on a tree in the subcritical, critical and supercritical phase. We do this by exploiting a mapping between continuum trees and Brownian excursions, and arrive at a diffusion equation with suitable boundary conditions. The exact solution to this equation can be conveniently represented as a characteristic function, from which the following distributions are clearly visible: Gaussian (subcritical), Kolmogorov-Smirnov (critical) and exponential (supercritical). In this way we provide an intuitive explanation for the result repor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03764","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":"2026-05-18T01:03:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1r8PHjdL4kW9xzvjcPAMLoVxlkkoP1R58Piw3hJa1ivbeZYJiQm4iZ63L+SE3eWtNwwHSmAlI5xMT9e5vuixBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:51:50.596831Z"},"content_sha256":"4a85574f73b36fd505b2bf7865fac03226aae1c7b81f4a4655543931c8f07a15","schema_version":"1.0","event_id":"sha256:4a85574f73b36fd505b2bf7865fac03226aae1c7b81f4a4655543931c8f07a15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X3TMZOTDDGYLZXLVNJJHHMZDMG/bundle.json","state_url":"https://pith.science/pith/X3TMZOTDDGYLZXLVNJJHHMZDMG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X3TMZOTDDGYLZXLVNJJHHMZDMG/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":"2026-06-01T13:51:50Z","links":{"resolver":"https://pith.science/pith/X3TMZOTDDGYLZXLVNJJHHMZDMG","bundle":"https://pith.science/pith/X3TMZOTDDGYLZXLVNJJHHMZDMG/bundle.json","state":"https://pith.science/pith/X3TMZOTDDGYLZXLVNJJHHMZDMG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X3TMZOTDDGYLZXLVNJJHHMZDMG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:X3TMZOTDDGYLZXLVNJJHHMZDMG","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":"ea5822e0fd7e89f59eef09646cfda993347d301c80d85cad1533b20fdedefe4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-12T21:29:15Z","title_canon_sha256":"94c90efafce9fb85d06ec9f2cc48f49df345decf854aefd18df14090c0f4a433"},"schema_version":"1.0","source":{"id":"1606.03764","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03764","created_at":"2026-05-18T01:03:18Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03764v1","created_at":"2026-05-18T01:03:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03764","created_at":"2026-05-18T01:03:18Z"},{"alias_kind":"pith_short_12","alias_value":"X3TMZOTDDGYL","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X3TMZOTDDGYLZXLV","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X3TMZOTD","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:4a85574f73b36fd505b2bf7865fac03226aae1c7b81f4a4655543931c8f07a15","target":"graph","created_at":"2026-05-18T01:03:18Z","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 calculate the distribution of the size of the percolating cluster on a tree in the subcritical, critical and supercritical phase. We do this by exploiting a mapping between continuum trees and Brownian excursions, and arrive at a diffusion equation with suitable boundary conditions. The exact solution to this equation can be conveniently represented as a characteristic function, from which the following distributions are clearly visible: Gaussian (subcritical), Kolmogorov-Smirnov (critical) and exponential (supercritical). In this way we provide an intuitive explanation for the result repor","authors_text":"Francesc Font-Clos, Nicholas R. Moloney","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-12T21:29:15Z","title":"Percolation on trees as a Brownian excursion: from Gaussian to Kolmogorov-Smirnov to Exponential statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03764","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:a8bcccf09c18471a871b70edfd4db417421ffdd9de1791fe68840ecd027c1143","target":"record","created_at":"2026-05-18T01:03:18Z","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":"ea5822e0fd7e89f59eef09646cfda993347d301c80d85cad1533b20fdedefe4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-06-12T21:29:15Z","title_canon_sha256":"94c90efafce9fb85d06ec9f2cc48f49df345decf854aefd18df14090c0f4a433"},"schema_version":"1.0","source":{"id":"1606.03764","kind":"arxiv","version":1}},"canonical_sha256":"bee6ccba6319b0bcdd756a5273b32361a316c75db5e4ae9d8e8bb71f1ac1e25d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bee6ccba6319b0bcdd756a5273b32361a316c75db5e4ae9d8e8bb71f1ac1e25d","first_computed_at":"2026-05-18T01:03:18.629062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:18.629062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V9MQj9aY+PdlMvOW5bLQ35yDbYoTyC7osY3WWHmEBvbnRc1XylssL+wVavyd50VQQtUL3CRMeDdUjRoFVNjVAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:18.629552Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8bcccf09c18471a871b70edfd4db417421ffdd9de1791fe68840ecd027c1143","sha256:4a85574f73b36fd505b2bf7865fac03226aae1c7b81f4a4655543931c8f07a15"],"state_sha256":"5fa65f7009439412916236e187239c4940698b4cba19b70ac5ea891100c0d94b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qo7fqlG0UriB4Xc+4NRF1zdnej+itz3tKbrQNbtyf4OLl1XB9GVwcxCE1WjzhTgLiDVgj40664e/sfOtHip4Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:51:50.598729Z","bundle_sha256":"89931018bcb4d657b6d49184ee1e82be239939937e4440b68ec971c228ce2806"}}