{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:NWVIKKVGPGXRXDOOXWQKBPWC2I","short_pith_number":"pith:NWVIKKVG","canonical_record":{"source":{"id":"2608.10066","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-08-10T18:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"c8a563449442cc99a0cf3c9df5b3d2fabccbc2fd0feae952c00e4d26a3908334","abstract_canon_sha256":"dbf8b61b6e57428040003bc504d30013159e6224d9d68c427bc6f353ebd018ed"},"schema_version":"1.0"},"canonical_sha256":"6daa852aa679af1b8dcebda0a0bec2d219ff84814da4f67fa65abd77cfcd1173","source":{"kind":"arxiv","id":"2608.10066","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.10066","created_at":"2026-08-12T00:22:42Z"},{"alias_kind":"arxiv_version","alias_value":"2608.10066v1","created_at":"2026-08-12T00:22:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.10066","created_at":"2026-08-12T00:22:42Z"},{"alias_kind":"pith_short_12","alias_value":"NWVIKKVGPGXR","created_at":"2026-08-12T00:22:42Z"},{"alias_kind":"pith_short_16","alias_value":"NWVIKKVGPGXRXDOO","created_at":"2026-08-12T00:22:42Z"},{"alias_kind":"pith_short_8","alias_value":"NWVIKKVG","created_at":"2026-08-12T00:22:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:NWVIKKVGPGXRXDOOXWQKBPWC2I","target":"record","payload":{"canonical_record":{"source":{"id":"2608.10066","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-08-10T18:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"c8a563449442cc99a0cf3c9df5b3d2fabccbc2fd0feae952c00e4d26a3908334","abstract_canon_sha256":"dbf8b61b6e57428040003bc504d30013159e6224d9d68c427bc6f353ebd018ed"},"schema_version":"1.0"},"canonical_sha256":"6daa852aa679af1b8dcebda0a0bec2d219ff84814da4f67fa65abd77cfcd1173","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-12T00:22:42.020168Z","signature_b64":"s1YVPyAcqjt7/GguNOzs2P3lUgf7nccDeRYapHoJyHZ7ph+H+Jd3C4u9H8zv8gsbC3IepkGiJs97mF1Ril7xAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6daa852aa679af1b8dcebda0a0bec2d219ff84814da4f67fa65abd77cfcd1173","last_reissued_at":"2026-08-12T00:22:42.018394Z","signature_status":"signed_v1","first_computed_at":"2026-08-12T00:22:42.018394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.10066","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":"2026-08-12T00:22:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LCHBO8dW4P6aqGnS0udz5AVvnNUzqQwQO/boZruFr9Qm3OtCIs3c/ibPjNNpdCaK5luwWr7tMgOwOmsUCdW/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T23:56:59.154585Z"},"content_sha256":"1868b933e4c30ca1c2ad27a461af97533c0f1456fa09f2073538794e2524ed87","schema_version":"1.0","event_id":"sha256:1868b933e4c30ca1c2ad27a461af97533c0f1456fa09f2073538794e2524ed87"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:NWVIKKVGPGXRXDOOXWQKBPWC2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Last Crossing in Excursion-Set Theory of Cosmic Reionization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Hanjue Zhu","submitted_at":"2026-08-10T18:00:00Z","abstract_excerpt":"I introduce the last crossing of the photon-counting barrier as a statistic for analytical models of cosmic reionization. Because ionizing galaxies are biased tracers of density and their photons propagate through gas of spatially varying opacity, the galaxy-IGM connection requires statistics beyond the global ionized fraction. The excursion-set model of Furlanetto et al. (2004) identifies the ionized-bubble scale around a point with the first crossing of a photon-counting barrier. I develop the last-crossing formalism and define the last-crossing scale, $R_\\ell$, as the smallest scale on whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10066","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.10066/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":"2026-08-12T00:22:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kuYss7El/hgp2SoFV2oF2/c4B/09PaMAgdHsptan8XIf8o9oqfIbe7rsKVPxtjZlSQWkBcfc5pFFTgNKnxcMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T23:56:59.155769Z"},"content_sha256":"b9a43929872192ee5b47eb68e745b894d75af75345a75ce09b407678944e7a44","schema_version":"1.0","event_id":"sha256:b9a43929872192ee5b47eb68e745b894d75af75345a75ce09b407678944e7a44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NWVIKKVGPGXRXDOOXWQKBPWC2I/bundle.json","state_url":"https://pith.science/pith/NWVIKKVGPGXRXDOOXWQKBPWC2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NWVIKKVGPGXRXDOOXWQKBPWC2I/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":"2026-08-14T23:56:59Z","links":{"resolver":"https://pith.science/pith/NWVIKKVGPGXRXDOOXWQKBPWC2I","bundle":"https://pith.science/pith/NWVIKKVGPGXRXDOOXWQKBPWC2I/bundle.json","state":"https://pith.science/pith/NWVIKKVGPGXRXDOOXWQKBPWC2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NWVIKKVGPGXRXDOOXWQKBPWC2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NWVIKKVGPGXRXDOOXWQKBPWC2I","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":"dbf8b61b6e57428040003bc504d30013159e6224d9d68c427bc6f353ebd018ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-08-10T18:00:00Z","title_canon_sha256":"c8a563449442cc99a0cf3c9df5b3d2fabccbc2fd0feae952c00e4d26a3908334"},"schema_version":"1.0","source":{"id":"2608.10066","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.10066","created_at":"2026-08-12T00:22:42Z"},{"alias_kind":"arxiv_version","alias_value":"2608.10066v1","created_at":"2026-08-12T00:22:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.10066","created_at":"2026-08-12T00:22:42Z"},{"alias_kind":"pith_short_12","alias_value":"NWVIKKVGPGXR","created_at":"2026-08-12T00:22:42Z"},{"alias_kind":"pith_short_16","alias_value":"NWVIKKVGPGXRXDOO","created_at":"2026-08-12T00:22:42Z"},{"alias_kind":"pith_short_8","alias_value":"NWVIKKVG","created_at":"2026-08-12T00:22:42Z"}],"graph_snapshots":[{"event_id":"sha256:b9a43929872192ee5b47eb68e745b894d75af75345a75ce09b407678944e7a44","target":"graph","created_at":"2026-08-12T00:22:42Z","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/2608.10066/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"I introduce the last crossing of the photon-counting barrier as a statistic for analytical models of cosmic reionization. Because ionizing galaxies are biased tracers of density and their photons propagate through gas of spatially varying opacity, the galaxy-IGM connection requires statistics beyond the global ionized fraction. The excursion-set model of Furlanetto et al. (2004) identifies the ionized-bubble scale around a point with the first crossing of a photon-counting barrier. I develop the last-crossing formalism and define the last-crossing scale, $R_\\ell$, as the smallest scale on whic","authors_text":"Hanjue Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-08-10T18:00:00Z","title":"The Last Crossing in Excursion-Set Theory of Cosmic Reionization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10066","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":"sha256:1868b933e4c30ca1c2ad27a461af97533c0f1456fa09f2073538794e2524ed87","target":"record","created_at":"2026-08-12T00:22:42Z","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":"dbf8b61b6e57428040003bc504d30013159e6224d9d68c427bc6f353ebd018ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-08-10T18:00:00Z","title_canon_sha256":"c8a563449442cc99a0cf3c9df5b3d2fabccbc2fd0feae952c00e4d26a3908334"},"schema_version":"1.0","source":{"id":"2608.10066","kind":"arxiv","version":1}},"canonical_sha256":"6daa852aa679af1b8dcebda0a0bec2d219ff84814da4f67fa65abd77cfcd1173","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6daa852aa679af1b8dcebda0a0bec2d219ff84814da4f67fa65abd77cfcd1173","first_computed_at":"2026-08-12T00:22:42.018394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-12T00:22:42.018394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s1YVPyAcqjt7/GguNOzs2P3lUgf7nccDeRYapHoJyHZ7ph+H+Jd3C4u9H8zv8gsbC3IepkGiJs97mF1Ril7xAw==","signature_status":"signed_v1","signed_at":"2026-08-12T00:22:42.020168Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.10066","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1868b933e4c30ca1c2ad27a461af97533c0f1456fa09f2073538794e2524ed87","sha256:b9a43929872192ee5b47eb68e745b894d75af75345a75ce09b407678944e7a44"],"state_sha256":"e0d94ed532ca540a650334fc7eef5cba16d52b5006d3f5dd9e4b68be5b334029"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hB1qMxVaQ31Kav51RCwsxonGbnQsulS38cl3Qn0GMw6dVrvoY5GOpnsBi0fA/h5ZerEujsWVkXvUtEdQ/m2HDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T23:56:59.163527Z","bundle_sha256":"85c16cbb1e40e33a4d6a5fc63adc6a5d345932811c923c4d3e685ce9379ccae9"}}