{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:RAG2DOQTWARHUI4R2XU5DQ42BV","short_pith_number":"pith:RAG2DOQT","canonical_record":{"source":{"id":"1006.2315","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-11T14:06:21Z","cross_cats_sorted":[],"title_canon_sha256":"8eac27b0d9871ca7945baef4f69c949c975d9bf637b339f6b4d0a5c741f41085","abstract_canon_sha256":"5dbe3c99743b4400dc342e1a50c31a12ae14fd8ea0b51d77c47321deaabf801d"},"schema_version":"1.0"},"canonical_sha256":"880da1ba13b0227a2391d5e9d1c39a0d6093f585d995492cb47ee37d1fa31170","source":{"kind":"arxiv","id":"1006.2315","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.2315","created_at":"2026-05-18T03:57:53Z"},{"alias_kind":"arxiv_version","alias_value":"1006.2315v2","created_at":"2026-05-18T03:57:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2315","created_at":"2026-05-18T03:57:53Z"},{"alias_kind":"pith_short_12","alias_value":"RAG2DOQTWARH","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RAG2DOQTWARHUI4R","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RAG2DOQT","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:RAG2DOQTWARHUI4R2XU5DQ42BV","target":"record","payload":{"canonical_record":{"source":{"id":"1006.2315","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-11T14:06:21Z","cross_cats_sorted":[],"title_canon_sha256":"8eac27b0d9871ca7945baef4f69c949c975d9bf637b339f6b4d0a5c741f41085","abstract_canon_sha256":"5dbe3c99743b4400dc342e1a50c31a12ae14fd8ea0b51d77c47321deaabf801d"},"schema_version":"1.0"},"canonical_sha256":"880da1ba13b0227a2391d5e9d1c39a0d6093f585d995492cb47ee37d1fa31170","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:53.706858Z","signature_b64":"GC99a9EprurzpTXtF/s+tFtpv27/S+bWk0bXpdLxPvlHCm72V/mjOL46TvpdNmOuAXCc+NbiTNGqjkc/uLjuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"880da1ba13b0227a2391d5e9d1c39a0d6093f585d995492cb47ee37d1fa31170","last_reissued_at":"2026-05-18T03:57:53.706087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:53.706087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.2315","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":"2026-05-18T03:57:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ww1QOivx7k3H6cB89yPPoNEwczu8XEfq5KqzXWsUMcXChB9l56DuK4rJ1GtJXCwMKGzLxgRHdobEEIBc1hNIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:14:42.073373Z"},"content_sha256":"f7b33d08b07b53688986fa4712980771ae0c6c3c938c96db3018343804c7a29f","schema_version":"1.0","event_id":"sha256:f7b33d08b07b53688986fa4712980771ae0c6c3c938c96db3018343804c7a29f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:RAG2DOQTWARHUI4R2XU5DQ42BV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A conditioning principle for Galton-Watson trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nadia Sidorova, Nathanael Berestycki, Peter Morters","submitted_at":"2010-06-11T14:06:21Z","abstract_excerpt":"We show that an infinite Galton-Watson tree, conditioned on its martingale limit being smaller than $\\eps$, converges as $\\eps\\downarrow 0$ in law to the regular $\\mu$-ary tree, where $\\mu$ is the essential minimum of the offspring distribution. This gives an example of entropic repulsion where the limit has no entropy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2315","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":"2026-05-18T03:57:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/hVV1++b2cbje0F18CMXHlLctY2MP5QH+RG3tQUu9S1RL1no95gsfUPZmrrvBR9cFLmuh9He8mnXPDa/ChVXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:14:42.074077Z"},"content_sha256":"1382dc599a37a25db83e748b39954ed7809d54b407ca22e652f5e2bdc7e01645","schema_version":"1.0","event_id":"sha256:1382dc599a37a25db83e748b39954ed7809d54b407ca22e652f5e2bdc7e01645"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RAG2DOQTWARHUI4R2XU5DQ42BV/bundle.json","state_url":"https://pith.science/pith/RAG2DOQTWARHUI4R2XU5DQ42BV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RAG2DOQTWARHUI4R2XU5DQ42BV/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":"2026-05-30T23:14:42Z","links":{"resolver":"https://pith.science/pith/RAG2DOQTWARHUI4R2XU5DQ42BV","bundle":"https://pith.science/pith/RAG2DOQTWARHUI4R2XU5DQ42BV/bundle.json","state":"https://pith.science/pith/RAG2DOQTWARHUI4R2XU5DQ42BV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RAG2DOQTWARHUI4R2XU5DQ42BV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RAG2DOQTWARHUI4R2XU5DQ42BV","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":"5dbe3c99743b4400dc342e1a50c31a12ae14fd8ea0b51d77c47321deaabf801d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-11T14:06:21Z","title_canon_sha256":"8eac27b0d9871ca7945baef4f69c949c975d9bf637b339f6b4d0a5c741f41085"},"schema_version":"1.0","source":{"id":"1006.2315","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.2315","created_at":"2026-05-18T03:57:53Z"},{"alias_kind":"arxiv_version","alias_value":"1006.2315v2","created_at":"2026-05-18T03:57:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2315","created_at":"2026-05-18T03:57:53Z"},{"alias_kind":"pith_short_12","alias_value":"RAG2DOQTWARH","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RAG2DOQTWARHUI4R","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RAG2DOQT","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:1382dc599a37a25db83e748b39954ed7809d54b407ca22e652f5e2bdc7e01645","target":"graph","created_at":"2026-05-18T03:57:53Z","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 show that an infinite Galton-Watson tree, conditioned on its martingale limit being smaller than $\\eps$, converges as $\\eps\\downarrow 0$ in law to the regular $\\mu$-ary tree, where $\\mu$ is the essential minimum of the offspring distribution. This gives an example of entropic repulsion where the limit has no entropy.","authors_text":"Nadia Sidorova, Nathanael Berestycki, Peter Morters","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-11T14:06:21Z","title":"A conditioning principle for Galton-Watson trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2315","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:f7b33d08b07b53688986fa4712980771ae0c6c3c938c96db3018343804c7a29f","target":"record","created_at":"2026-05-18T03:57:53Z","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":"5dbe3c99743b4400dc342e1a50c31a12ae14fd8ea0b51d77c47321deaabf801d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-11T14:06:21Z","title_canon_sha256":"8eac27b0d9871ca7945baef4f69c949c975d9bf637b339f6b4d0a5c741f41085"},"schema_version":"1.0","source":{"id":"1006.2315","kind":"arxiv","version":2}},"canonical_sha256":"880da1ba13b0227a2391d5e9d1c39a0d6093f585d995492cb47ee37d1fa31170","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"880da1ba13b0227a2391d5e9d1c39a0d6093f585d995492cb47ee37d1fa31170","first_computed_at":"2026-05-18T03:57:53.706087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:53.706087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GC99a9EprurzpTXtF/s+tFtpv27/S+bWk0bXpdLxPvlHCm72V/mjOL46TvpdNmOuAXCc+NbiTNGqjkc/uLjuBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:53.706858Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.2315","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7b33d08b07b53688986fa4712980771ae0c6c3c938c96db3018343804c7a29f","sha256:1382dc599a37a25db83e748b39954ed7809d54b407ca22e652f5e2bdc7e01645"],"state_sha256":"dcbc93c89112c5be5bbbdc71dda877482459e843c33e45be1e715ab46ce27185"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rNN2NFOL2DXvwEzUouvIyrWoQ0dXPv/HXZtZcBGiY0FZogk3Ybe/1hLB7f4L+YXBbbdB0cueclQ3A1WjP/lZCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:14:42.077984Z","bundle_sha256":"42d0e7201901a9adb13d4c24df33ab6706b5a588bf5b6fa8b6f762c118bbcf7e"}}