{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ABKOYI7TLOFSS4B6F7GR6N5ZXS","short_pith_number":"pith:ABKOYI7T","canonical_record":{"source":{"id":"1908.07120","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-20T01:12:45Z","cross_cats_sorted":[],"title_canon_sha256":"5054c24a0e93015c288be0d4389379ec67093b557d218c2d24ad02aaf5dd23d1","abstract_canon_sha256":"58fc772b584cb5dfb8afa9d7fa98c600ee23064bd5c3194269ede71d05465a65"},"schema_version":"1.0"},"canonical_sha256":"0054ec23f35b8b29703e2fcd1f37b9bc800145995d813cd07208ebe7b2889e6a","source":{"kind":"arxiv","id":"1908.07120","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07120","created_at":"2026-07-05T03:33:36Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07120v3","created_at":"2026-07-05T03:33:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07120","created_at":"2026-07-05T03:33:36Z"},{"alias_kind":"pith_short_12","alias_value":"ABKOYI7TLOFS","created_at":"2026-07-05T03:33:36Z"},{"alias_kind":"pith_short_16","alias_value":"ABKOYI7TLOFSS4B6","created_at":"2026-07-05T03:33:36Z"},{"alias_kind":"pith_short_8","alias_value":"ABKOYI7T","created_at":"2026-07-05T03:33:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ABKOYI7TLOFSS4B6F7GR6N5ZXS","target":"record","payload":{"canonical_record":{"source":{"id":"1908.07120","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-20T01:12:45Z","cross_cats_sorted":[],"title_canon_sha256":"5054c24a0e93015c288be0d4389379ec67093b557d218c2d24ad02aaf5dd23d1","abstract_canon_sha256":"58fc772b584cb5dfb8afa9d7fa98c600ee23064bd5c3194269ede71d05465a65"},"schema_version":"1.0"},"canonical_sha256":"0054ec23f35b8b29703e2fcd1f37b9bc800145995d813cd07208ebe7b2889e6a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:33:36.640688Z","signature_b64":"W35Wmc8DVdZwEdIRAuB231kxstnNy/GYEHqjnS0dD1QacY09o15+MPdlQfJKJ7z20IaJS0wdWL2sTQwAcTMiCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0054ec23f35b8b29703e2fcd1f37b9bc800145995d813cd07208ebe7b2889e6a","last_reissued_at":"2026-07-05T03:33:36.640150Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:33:36.640150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.07120","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:33:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mE2c8L39H8Jjv4F4pkNBFlZiHUOkO5Ins71XzaxNcLuyW2PvTnCQNLhAvAn4MGkuNl1DUqbM+urLvGAzyD0DBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:24:26.992578Z"},"content_sha256":"bd05b51fe743a0d274b7ada4fd8cfea9a154829a9549cf3d7b1f916256603cb4","schema_version":"1.0","event_id":"sha256:bd05b51fe743a0d274b7ada4fd8cfea9a154829a9549cf3d7b1f916256603cb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ABKOYI7TLOFSS4B6F7GR6N5ZXS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continuum models of directed polymers on disordered diamond fractals in the critical case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jeremy Clark","submitted_at":"2019-08-20T01:12:45Z","abstract_excerpt":"We construct and study a family random continuum polymer measures $\\mathbf{M}_{r}$ corresponding to limiting partition function laws recently derived in a weak-coupling regime of polymer models on hierarchical graphs with marginally relevant disorder. The continuum polymers, which we refer to as directed paths, are identified with isometric embeddings of the unit interval $[0,1]$ into a compact diamond fractal with Hausdorff dimension two, and there is a natural 'uniform' probability measure, $\\mu$, over the space of directed paths, $\\Gamma$. Realizations of the random path measures $\\mathbf{M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07120","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07120/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:33:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kuCfeZ/mOvjlnFY2Gyjw/lBFi5m7oBXecfQg650xHG2nDoPtQhbQELll9AUqH7BjAkymmVud0DJRhBIhNe4UAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:24:26.993790Z"},"content_sha256":"e7050c30495a50082438b6cc330a0f0c70fb5df20e4ed1bf9a95e8e192f67354","schema_version":"1.0","event_id":"sha256:e7050c30495a50082438b6cc330a0f0c70fb5df20e4ed1bf9a95e8e192f67354"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABKOYI7TLOFSS4B6F7GR6N5ZXS/bundle.json","state_url":"https://pith.science/pith/ABKOYI7TLOFSS4B6F7GR6N5ZXS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABKOYI7TLOFSS4B6F7GR6N5ZXS/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":"2026-08-16T15:24:27Z","links":{"resolver":"https://pith.science/pith/ABKOYI7TLOFSS4B6F7GR6N5ZXS","bundle":"https://pith.science/pith/ABKOYI7TLOFSS4B6F7GR6N5ZXS/bundle.json","state":"https://pith.science/pith/ABKOYI7TLOFSS4B6F7GR6N5ZXS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABKOYI7TLOFSS4B6F7GR6N5ZXS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ABKOYI7TLOFSS4B6F7GR6N5ZXS","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":"58fc772b584cb5dfb8afa9d7fa98c600ee23064bd5c3194269ede71d05465a65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-20T01:12:45Z","title_canon_sha256":"5054c24a0e93015c288be0d4389379ec67093b557d218c2d24ad02aaf5dd23d1"},"schema_version":"1.0","source":{"id":"1908.07120","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07120","created_at":"2026-07-05T03:33:36Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07120v3","created_at":"2026-07-05T03:33:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07120","created_at":"2026-07-05T03:33:36Z"},{"alias_kind":"pith_short_12","alias_value":"ABKOYI7TLOFS","created_at":"2026-07-05T03:33:36Z"},{"alias_kind":"pith_short_16","alias_value":"ABKOYI7TLOFSS4B6","created_at":"2026-07-05T03:33:36Z"},{"alias_kind":"pith_short_8","alias_value":"ABKOYI7T","created_at":"2026-07-05T03:33:36Z"}],"graph_snapshots":[{"event_id":"sha256:e7050c30495a50082438b6cc330a0f0c70fb5df20e4ed1bf9a95e8e192f67354","target":"graph","created_at":"2026-07-05T03:33:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.07120/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct and study a family random continuum polymer measures $\\mathbf{M}_{r}$ corresponding to limiting partition function laws recently derived in a weak-coupling regime of polymer models on hierarchical graphs with marginally relevant disorder. The continuum polymers, which we refer to as directed paths, are identified with isometric embeddings of the unit interval $[0,1]$ into a compact diamond fractal with Hausdorff dimension two, and there is a natural 'uniform' probability measure, $\\mu$, over the space of directed paths, $\\Gamma$. Realizations of the random path measures $\\mathbf{M","authors_text":"Jeremy Clark","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-20T01:12:45Z","title":"Continuum models of directed polymers on disordered diamond fractals in the critical case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07120","kind":"arxiv","version":3},"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:bd05b51fe743a0d274b7ada4fd8cfea9a154829a9549cf3d7b1f916256603cb4","target":"record","created_at":"2026-07-05T03:33:36Z","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":"58fc772b584cb5dfb8afa9d7fa98c600ee23064bd5c3194269ede71d05465a65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-20T01:12:45Z","title_canon_sha256":"5054c24a0e93015c288be0d4389379ec67093b557d218c2d24ad02aaf5dd23d1"},"schema_version":"1.0","source":{"id":"1908.07120","kind":"arxiv","version":3}},"canonical_sha256":"0054ec23f35b8b29703e2fcd1f37b9bc800145995d813cd07208ebe7b2889e6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0054ec23f35b8b29703e2fcd1f37b9bc800145995d813cd07208ebe7b2889e6a","first_computed_at":"2026-07-05T03:33:36.640150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:33:36.640150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W35Wmc8DVdZwEdIRAuB231kxstnNy/GYEHqjnS0dD1QacY09o15+MPdlQfJKJ7z20IaJS0wdWL2sTQwAcTMiCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:33:36.640688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07120","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd05b51fe743a0d274b7ada4fd8cfea9a154829a9549cf3d7b1f916256603cb4","sha256:e7050c30495a50082438b6cc330a0f0c70fb5df20e4ed1bf9a95e8e192f67354"],"state_sha256":"d37791c2f6931113c9abd8e63a09c6cd368c0b075c75fb2502d98d954abe697f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6DFuB/LoHepF4yEtnPfeznpMWF+wy8J/5VwG8UFo8MeZ8l9nlkOKSuXZ+oRRaZjKT5qL+mw5FG8w4k4Ceg5nBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T15:24:27.006259Z","bundle_sha256":"d7f1b5ad5f1406091f5edcebc5386ed36b9b02754929f1c79b2e94deb114b90e"}}