{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:Y2XBIFUDDUQ5PNUW6RYWLC7YB2","short_pith_number":"pith:Y2XBIFUD","canonical_record":{"source":{"id":"1703.09792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-28T20:37:49Z","cross_cats_sorted":[],"title_canon_sha256":"ababbe4080c97dd0cdc2050d18a89289448568a8f2eafdc079fd2d28d38e03eb","abstract_canon_sha256":"f507173935da56644fcc0f8b5caf6118c3aa6c81e40edddce280f477e27b3120"},"schema_version":"1.0"},"canonical_sha256":"c6ae1416831d21d7b696f471658bf80eb2fe0bfd31a677bcfd97effa4b5bad5d","source":{"kind":"arxiv","id":"1703.09792","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.09792","created_at":"2026-05-18T00:47:39Z"},{"alias_kind":"arxiv_version","alias_value":"1703.09792v1","created_at":"2026-05-18T00:47:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09792","created_at":"2026-05-18T00:47:39Z"},{"alias_kind":"pith_short_12","alias_value":"Y2XBIFUDDUQ5","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"Y2XBIFUDDUQ5PNUW","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"Y2XBIFUD","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:Y2XBIFUDDUQ5PNUW6RYWLC7YB2","target":"record","payload":{"canonical_record":{"source":{"id":"1703.09792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-28T20:37:49Z","cross_cats_sorted":[],"title_canon_sha256":"ababbe4080c97dd0cdc2050d18a89289448568a8f2eafdc079fd2d28d38e03eb","abstract_canon_sha256":"f507173935da56644fcc0f8b5caf6118c3aa6c81e40edddce280f477e27b3120"},"schema_version":"1.0"},"canonical_sha256":"c6ae1416831d21d7b696f471658bf80eb2fe0bfd31a677bcfd97effa4b5bad5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:39.459662Z","signature_b64":"Zc1gUuMoL+6gIgUsmCG3evZoMZ0PRddINlPGxOhJeay/sxKzCQtyq4bVk6cfuhvpPGdYGrXR8YoGJjXQIF8LDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6ae1416831d21d7b696f471658bf80eb2fe0bfd31a677bcfd97effa4b5bad5d","last_reissued_at":"2026-05-18T00:47:39.458946Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:39.458946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.09792","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":"2026-05-18T00:47:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+N7SEq0UNhVLn2g42p4FFRewcuDgeN/8E05B5tiDqHlDLoDS2A8FNz/uGj9678vSI2ZQxuKzKpHqMEFUNmYyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:50:40.055087Z"},"content_sha256":"2e19067fda918673d8a701bcc796d77616ef5beb52f70f29076935fcc49daa96","schema_version":"1.0","event_id":"sha256:2e19067fda918673d8a701bcc796d77616ef5beb52f70f29076935fcc49daa96"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:Y2XBIFUDDUQ5PNUW6RYWLC7YB2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The near-critical Gibbs measure of the branching random walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michel Pain","submitted_at":"2017-03-28T20:37:49Z","abstract_excerpt":"Consider the supercritical branching random walk on the real line in the boundary case and the associated Gibbs measure $\\nu_{n,\\beta}$ on the $n^\\text{th}$ generation, which is also the polymer measure on a disordered tree with inverse temperature $\\beta$. The convergence of the partition function $W_{n,\\beta}$, after rescaling, towards a nontrivial limit has been proved by A\\\"{\\i}d\\'ekon and Shi in the critical case $\\beta = 1$ and by Madaule when $\\beta >1$. We study here the near-critical case, where $\\beta_n \\to 1$, and prove the convergence of $W_{n,\\beta_n}$, after rescaling, towards a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09792","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":"2026-05-18T00:47:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YgOIZt3T96XCvgQjhang3wQxBYDYgzX3Rf0xyqKTNIcqfoYqgqsrrBtMwbgAbrMUwLnv3KD1clwnMC3Tcu0dAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:50:40.055445Z"},"content_sha256":"fad4211c67a3e61aef666e7d0cc125d6860033ad322d01525442c3fa8f0057f3","schema_version":"1.0","event_id":"sha256:fad4211c67a3e61aef666e7d0cc125d6860033ad322d01525442c3fa8f0057f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y2XBIFUDDUQ5PNUW6RYWLC7YB2/bundle.json","state_url":"https://pith.science/pith/Y2XBIFUDDUQ5PNUW6RYWLC7YB2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y2XBIFUDDUQ5PNUW6RYWLC7YB2/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":"2026-06-27T13:50:40Z","links":{"resolver":"https://pith.science/pith/Y2XBIFUDDUQ5PNUW6RYWLC7YB2","bundle":"https://pith.science/pith/Y2XBIFUDDUQ5PNUW6RYWLC7YB2/bundle.json","state":"https://pith.science/pith/Y2XBIFUDDUQ5PNUW6RYWLC7YB2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y2XBIFUDDUQ5PNUW6RYWLC7YB2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Y2XBIFUDDUQ5PNUW6RYWLC7YB2","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":"f507173935da56644fcc0f8b5caf6118c3aa6c81e40edddce280f477e27b3120","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-28T20:37:49Z","title_canon_sha256":"ababbe4080c97dd0cdc2050d18a89289448568a8f2eafdc079fd2d28d38e03eb"},"schema_version":"1.0","source":{"id":"1703.09792","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.09792","created_at":"2026-05-18T00:47:39Z"},{"alias_kind":"arxiv_version","alias_value":"1703.09792v1","created_at":"2026-05-18T00:47:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09792","created_at":"2026-05-18T00:47:39Z"},{"alias_kind":"pith_short_12","alias_value":"Y2XBIFUDDUQ5","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"Y2XBIFUDDUQ5PNUW","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"Y2XBIFUD","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:fad4211c67a3e61aef666e7d0cc125d6860033ad322d01525442c3fa8f0057f3","target":"graph","created_at":"2026-05-18T00:47:39Z","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":"Consider the supercritical branching random walk on the real line in the boundary case and the associated Gibbs measure $\\nu_{n,\\beta}$ on the $n^\\text{th}$ generation, which is also the polymer measure on a disordered tree with inverse temperature $\\beta$. The convergence of the partition function $W_{n,\\beta}$, after rescaling, towards a nontrivial limit has been proved by A\\\"{\\i}d\\'ekon and Shi in the critical case $\\beta = 1$ and by Madaule when $\\beta >1$. We study here the near-critical case, where $\\beta_n \\to 1$, and prove the convergence of $W_{n,\\beta_n}$, after rescaling, towards a ","authors_text":"Michel Pain","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-28T20:37:49Z","title":"The near-critical Gibbs measure of the branching random walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09792","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":"sha256:2e19067fda918673d8a701bcc796d77616ef5beb52f70f29076935fcc49daa96","target":"record","created_at":"2026-05-18T00:47:39Z","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":"f507173935da56644fcc0f8b5caf6118c3aa6c81e40edddce280f477e27b3120","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-28T20:37:49Z","title_canon_sha256":"ababbe4080c97dd0cdc2050d18a89289448568a8f2eafdc079fd2d28d38e03eb"},"schema_version":"1.0","source":{"id":"1703.09792","kind":"arxiv","version":1}},"canonical_sha256":"c6ae1416831d21d7b696f471658bf80eb2fe0bfd31a677bcfd97effa4b5bad5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6ae1416831d21d7b696f471658bf80eb2fe0bfd31a677bcfd97effa4b5bad5d","first_computed_at":"2026-05-18T00:47:39.458946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:39.458946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zc1gUuMoL+6gIgUsmCG3evZoMZ0PRddINlPGxOhJeay/sxKzCQtyq4bVk6cfuhvpPGdYGrXR8YoGJjXQIF8LDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:39.459662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.09792","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e19067fda918673d8a701bcc796d77616ef5beb52f70f29076935fcc49daa96","sha256:fad4211c67a3e61aef666e7d0cc125d6860033ad322d01525442c3fa8f0057f3"],"state_sha256":"1b11cfdfb6e70a465ad09d2385d8f3cf2bd0ce311d64b531e148c53b21cb079a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ckZ/ipNzhmbRjL2ZSKPZU1lbrDgU88EJYXIIREU78Fve4t+7yg4De+40ouzEZVxwDktZ4ACIsNlf6yRBIgseAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T13:50:40.057454Z","bundle_sha256":"4b76fa246715932fd18ec3c3eeea48b970bd95eef32337b845050cbdff17383a"}}