{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WWEL3J2PGCFAMVAJV37TW6Q5RI","short_pith_number":"pith:WWEL3J2P","canonical_record":{"source":{"id":"1811.08058","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-20T03:53:48Z","cross_cats_sorted":[],"title_canon_sha256":"972c9a8b49b3fa1114f4ca1622ae8fef1008872090673615ea386947f0ebb3ec","abstract_canon_sha256":"cbdef600ee76b70f13e8b6d67afa84e7cc73591d66162e48f7e6e241cc8d2188"},"schema_version":"1.0"},"canonical_sha256":"b588bda74f308a065409aeff3b7a1d8a0d3ae63b3489ee73a3a609f3f883401a","source":{"kind":"arxiv","id":"1811.08058","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.08058","created_at":"2026-05-18T00:00:16Z"},{"alias_kind":"arxiv_version","alias_value":"1811.08058v1","created_at":"2026-05-18T00:00:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08058","created_at":"2026-05-18T00:00:16Z"},{"alias_kind":"pith_short_12","alias_value":"WWEL3J2PGCFA","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WWEL3J2PGCFAMVAJ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WWEL3J2P","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WWEL3J2PGCFAMVAJV37TW6Q5RI","target":"record","payload":{"canonical_record":{"source":{"id":"1811.08058","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-20T03:53:48Z","cross_cats_sorted":[],"title_canon_sha256":"972c9a8b49b3fa1114f4ca1622ae8fef1008872090673615ea386947f0ebb3ec","abstract_canon_sha256":"cbdef600ee76b70f13e8b6d67afa84e7cc73591d66162e48f7e6e241cc8d2188"},"schema_version":"1.0"},"canonical_sha256":"b588bda74f308a065409aeff3b7a1d8a0d3ae63b3489ee73a3a609f3f883401a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:16.978282Z","signature_b64":"X7Sy3pIF8SGQJWzVs1ZCxrvCi12uyJdtdYIUlNj36CTxK7rt5Ap5C6PX0ltwxoKc7vKEr//Y/MxCxidMKrqXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b588bda74f308a065409aeff3b7a1d8a0d3ae63b3489ee73a3a609f3f883401a","last_reissued_at":"2026-05-18T00:00:16.977688Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:16.977688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.08058","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":"2026-05-18T00:00:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vxhapxCh7dKxlC+bIhdqhWqRWvdAEwueuUWlaj3ndHJhvtxZQUT00EP5k/8+GqU8XTET3eW3J1r0f9V29zqaDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:35:51.165661Z"},"content_sha256":"31fd2c0047f83cb0db95438b4c8db35b3db5ba1945b1b708832eb24958d0a400","schema_version":"1.0","event_id":"sha256:31fd2c0047f83cb0db95438b4c8db35b3db5ba1945b1b708832eb24958d0a400"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WWEL3J2PGCFAMVAJV37TW6Q5RI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The branching-ruin number as critical parameter of random processes on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrea Collevecchio, Cong Bang Huynh, Daniel Kious","submitted_at":"2018-11-20T03:53:48Z","abstract_excerpt":"The branching-ruin number of a tree, which describes its asymptotic growth and geometry, can be seen as a polynomial version of the branching number. This quantity was defined by Collevecchio, Kious and Sidoravicius (2018) in order to understand the phase transitions of the once-reinforced random walk (ORRW) on trees. Strikingly, this number was proved to be equal to the critical parameter of ORRW on trees. In this paper, we continue the investigation of the link between the branching-ruin number and the criticality of random processes on trees. First, we study random walks on random conductan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08058","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":"2026-05-18T00:00:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ESzfbNPunSjehUuEs28NoicZx3+QpxFvASTwd4Wyxh0IwJb2qZ2x1eT7Pv+P9czhX5XMdXSPAcw7moJi072VCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:35:51.166281Z"},"content_sha256":"4b4bc0f07e70ee71829d9ae612151758ba1569041c4990f5124863c502bd3065","schema_version":"1.0","event_id":"sha256:4b4bc0f07e70ee71829d9ae612151758ba1569041c4990f5124863c502bd3065"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WWEL3J2PGCFAMVAJV37TW6Q5RI/bundle.json","state_url":"https://pith.science/pith/WWEL3J2PGCFAMVAJV37TW6Q5RI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WWEL3J2PGCFAMVAJV37TW6Q5RI/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":"2026-05-25T19:35:51Z","links":{"resolver":"https://pith.science/pith/WWEL3J2PGCFAMVAJV37TW6Q5RI","bundle":"https://pith.science/pith/WWEL3J2PGCFAMVAJV37TW6Q5RI/bundle.json","state":"https://pith.science/pith/WWEL3J2PGCFAMVAJV37TW6Q5RI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WWEL3J2PGCFAMVAJV37TW6Q5RI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WWEL3J2PGCFAMVAJV37TW6Q5RI","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":"cbdef600ee76b70f13e8b6d67afa84e7cc73591d66162e48f7e6e241cc8d2188","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-20T03:53:48Z","title_canon_sha256":"972c9a8b49b3fa1114f4ca1622ae8fef1008872090673615ea386947f0ebb3ec"},"schema_version":"1.0","source":{"id":"1811.08058","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.08058","created_at":"2026-05-18T00:00:16Z"},{"alias_kind":"arxiv_version","alias_value":"1811.08058v1","created_at":"2026-05-18T00:00:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08058","created_at":"2026-05-18T00:00:16Z"},{"alias_kind":"pith_short_12","alias_value":"WWEL3J2PGCFA","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WWEL3J2PGCFAMVAJ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WWEL3J2P","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:4b4bc0f07e70ee71829d9ae612151758ba1569041c4990f5124863c502bd3065","target":"graph","created_at":"2026-05-18T00:00:16Z","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":"The branching-ruin number of a tree, which describes its asymptotic growth and geometry, can be seen as a polynomial version of the branching number. This quantity was defined by Collevecchio, Kious and Sidoravicius (2018) in order to understand the phase transitions of the once-reinforced random walk (ORRW) on trees. Strikingly, this number was proved to be equal to the critical parameter of ORRW on trees. In this paper, we continue the investigation of the link between the branching-ruin number and the criticality of random processes on trees. First, we study random walks on random conductan","authors_text":"Andrea Collevecchio, Cong Bang Huynh, Daniel Kious","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-20T03:53:48Z","title":"The branching-ruin number as critical parameter of random processes on trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08058","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":"sha256:31fd2c0047f83cb0db95438b4c8db35b3db5ba1945b1b708832eb24958d0a400","target":"record","created_at":"2026-05-18T00:00:16Z","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":"cbdef600ee76b70f13e8b6d67afa84e7cc73591d66162e48f7e6e241cc8d2188","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-20T03:53:48Z","title_canon_sha256":"972c9a8b49b3fa1114f4ca1622ae8fef1008872090673615ea386947f0ebb3ec"},"schema_version":"1.0","source":{"id":"1811.08058","kind":"arxiv","version":1}},"canonical_sha256":"b588bda74f308a065409aeff3b7a1d8a0d3ae63b3489ee73a3a609f3f883401a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b588bda74f308a065409aeff3b7a1d8a0d3ae63b3489ee73a3a609f3f883401a","first_computed_at":"2026-05-18T00:00:16.977688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:16.977688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X7Sy3pIF8SGQJWzVs1ZCxrvCi12uyJdtdYIUlNj36CTxK7rt5Ap5C6PX0ltwxoKc7vKEr//Y/MxCxidMKrqXDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:16.978282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.08058","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31fd2c0047f83cb0db95438b4c8db35b3db5ba1945b1b708832eb24958d0a400","sha256:4b4bc0f07e70ee71829d9ae612151758ba1569041c4990f5124863c502bd3065"],"state_sha256":"a11bd1205752f3b13dd311a62d46f46dce923015b183ce564bc0db22426e5baa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3wC9StjNBxKzWS0+GmHY7J8DApWZDEjOUH0u5dgQSZZ1f3/a1j21PiE2RB5QPxlhVBc3vTlmoGAPHj9vuUgWCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:35:51.169950Z","bundle_sha256":"7e1ebcf632e5271f080882d2f42b1e018ecc1364b06daa54b861b31278264a99"}}