{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:I5WMSFTE6JNFWRI45ZVPUWJBNK","short_pith_number":"pith:I5WMSFTE","canonical_record":{"source":{"id":"2607.00290","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.optics","submitted_at":"2026-07-01T00:35:47Z","cross_cats_sorted":[],"title_canon_sha256":"cf5df01738cdf32497df3ba73088250bea43fce37cce4ba3d1fe458b23918958","abstract_canon_sha256":"26eac374dfd9121136ed49627388a2bb75e20a4d963f6fe27c35516e0c23c855"},"schema_version":"1.0"},"canonical_sha256":"476cc91664f25a5b451cee6afa59216ab8ebfdd47656d14458fe605a54102856","source":{"kind":"arxiv","id":"2607.00290","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00290","created_at":"2026-07-02T00:18:43Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00290v1","created_at":"2026-07-02T00:18:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00290","created_at":"2026-07-02T00:18:43Z"},{"alias_kind":"pith_short_12","alias_value":"I5WMSFTE6JNF","created_at":"2026-07-02T00:18:43Z"},{"alias_kind":"pith_short_16","alias_value":"I5WMSFTE6JNFWRI4","created_at":"2026-07-02T00:18:43Z"},{"alias_kind":"pith_short_8","alias_value":"I5WMSFTE","created_at":"2026-07-02T00:18:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:I5WMSFTE6JNFWRI45ZVPUWJBNK","target":"record","payload":{"canonical_record":{"source":{"id":"2607.00290","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.optics","submitted_at":"2026-07-01T00:35:47Z","cross_cats_sorted":[],"title_canon_sha256":"cf5df01738cdf32497df3ba73088250bea43fce37cce4ba3d1fe458b23918958","abstract_canon_sha256":"26eac374dfd9121136ed49627388a2bb75e20a4d963f6fe27c35516e0c23c855"},"schema_version":"1.0"},"canonical_sha256":"476cc91664f25a5b451cee6afa59216ab8ebfdd47656d14458fe605a54102856","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T00:18:43.124353Z","signature_b64":"P7kxRH5+nU2ujV3zMXacY8bc5ecOy+9SI5OuGGGRV46utvdB0vGKpddS5wHwoM8KLXqN3OSa1Vl0lwk8WI4eBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"476cc91664f25a5b451cee6afa59216ab8ebfdd47656d14458fe605a54102856","last_reissued_at":"2026-07-02T00:18:43.123844Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T00:18:43.123844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.00290","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":"2026-07-02T00:18:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WaFWRb2xMDl6K0td/LiBMkpUgdrM0n3nJPtJjF6Jy36n1UUZMNZZqa5I2XsslgmT0rsyJ1FJfrG04nXWg3sVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T01:21:43.772732Z"},"content_sha256":"e1572e00f6e226605076b6d9c2791f61810a2d645e3417946abe017ea4b5048e","schema_version":"1.0","event_id":"sha256:e1572e00f6e226605076b6d9c2791f61810a2d645e3417946abe017ea4b5048e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:I5WMSFTE6JNFWRI45ZVPUWJBNK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite slab first passage statistics of Henyey Greenstein scattering","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"physics.optics","authors_text":"Claude Zeller, Robert Cordery","submitted_at":"2026-07-01T00:35:47Z","abstract_excerpt":"A photon entering a plane parallel scattering slab performs a random walk and eventually escapes through one of the two faces or is absorbed. The scattering distribution is a Henyey Greenstein phase function and the step length distribution is exponential. The central result of this paper is that the reflectance, transmittance, absorptance, and emergent angular distributions can all be expressed in terms of the first passage statistics of the walk. Two approaches are used. In the Monte Carlo MC approach, an extremely long random walk with many steps is efficiently generated without regard to a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00290","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/2607.00290/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":"2026-07-02T00:18:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m3ph5IFEZEzZpXQ1ZCpcuEDoaAqi5Nh77VDEkffI8as8nqKs5+1SlJ5JrMlFt5DNt4Ku715vl9wDIuLdzg41CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T01:21:43.773319Z"},"content_sha256":"1766253469decc7b9ec67626dfe4f007920c5a70f40618c1c9ad05a000fdd4b1","schema_version":"1.0","event_id":"sha256:1766253469decc7b9ec67626dfe4f007920c5a70f40618c1c9ad05a000fdd4b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I5WMSFTE6JNFWRI45ZVPUWJBNK/bundle.json","state_url":"https://pith.science/pith/I5WMSFTE6JNFWRI45ZVPUWJBNK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I5WMSFTE6JNFWRI45ZVPUWJBNK/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":"2026-08-18T01:21:43Z","links":{"resolver":"https://pith.science/pith/I5WMSFTE6JNFWRI45ZVPUWJBNK","bundle":"https://pith.science/pith/I5WMSFTE6JNFWRI45ZVPUWJBNK/bundle.json","state":"https://pith.science/pith/I5WMSFTE6JNFWRI45ZVPUWJBNK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I5WMSFTE6JNFWRI45ZVPUWJBNK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:I5WMSFTE6JNFWRI45ZVPUWJBNK","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":"26eac374dfd9121136ed49627388a2bb75e20a4d963f6fe27c35516e0c23c855","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.optics","submitted_at":"2026-07-01T00:35:47Z","title_canon_sha256":"cf5df01738cdf32497df3ba73088250bea43fce37cce4ba3d1fe458b23918958"},"schema_version":"1.0","source":{"id":"2607.00290","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00290","created_at":"2026-07-02T00:18:43Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00290v1","created_at":"2026-07-02T00:18:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00290","created_at":"2026-07-02T00:18:43Z"},{"alias_kind":"pith_short_12","alias_value":"I5WMSFTE6JNF","created_at":"2026-07-02T00:18:43Z"},{"alias_kind":"pith_short_16","alias_value":"I5WMSFTE6JNFWRI4","created_at":"2026-07-02T00:18:43Z"},{"alias_kind":"pith_short_8","alias_value":"I5WMSFTE","created_at":"2026-07-02T00:18:43Z"}],"graph_snapshots":[{"event_id":"sha256:1766253469decc7b9ec67626dfe4f007920c5a70f40618c1c9ad05a000fdd4b1","target":"graph","created_at":"2026-07-02T00:18:43Z","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/2607.00290/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A photon entering a plane parallel scattering slab performs a random walk and eventually escapes through one of the two faces or is absorbed. The scattering distribution is a Henyey Greenstein phase function and the step length distribution is exponential. The central result of this paper is that the reflectance, transmittance, absorptance, and emergent angular distributions can all be expressed in terms of the first passage statistics of the walk. Two approaches are used. In the Monte Carlo MC approach, an extremely long random walk with many steps is efficiently generated without regard to a","authors_text":"Claude Zeller, Robert Cordery","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.optics","submitted_at":"2026-07-01T00:35:47Z","title":"Finite slab first passage statistics of Henyey Greenstein scattering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00290","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:e1572e00f6e226605076b6d9c2791f61810a2d645e3417946abe017ea4b5048e","target":"record","created_at":"2026-07-02T00:18:43Z","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":"26eac374dfd9121136ed49627388a2bb75e20a4d963f6fe27c35516e0c23c855","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.optics","submitted_at":"2026-07-01T00:35:47Z","title_canon_sha256":"cf5df01738cdf32497df3ba73088250bea43fce37cce4ba3d1fe458b23918958"},"schema_version":"1.0","source":{"id":"2607.00290","kind":"arxiv","version":1}},"canonical_sha256":"476cc91664f25a5b451cee6afa59216ab8ebfdd47656d14458fe605a54102856","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"476cc91664f25a5b451cee6afa59216ab8ebfdd47656d14458fe605a54102856","first_computed_at":"2026-07-02T00:18:43.123844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T00:18:43.123844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P7kxRH5+nU2ujV3zMXacY8bc5ecOy+9SI5OuGGGRV46utvdB0vGKpddS5wHwoM8KLXqN3OSa1Vl0lwk8WI4eBw==","signature_status":"signed_v1","signed_at":"2026-07-02T00:18:43.124353Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.00290","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1572e00f6e226605076b6d9c2791f61810a2d645e3417946abe017ea4b5048e","sha256:1766253469decc7b9ec67626dfe4f007920c5a70f40618c1c9ad05a000fdd4b1"],"state_sha256":"0d0877c4bc483eea62dbab16daac40c5fc8dd4aed6d75600c31ad0171632ef27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c33qvilXKKT13OCuNRsmg7Uj7nWPMSc0Zt6kNAUlccmAuHzImCSqenWa3PO1LOFycJwswFr8UnB94QqGP85PCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T01:21:43.777551Z","bundle_sha256":"f22111ad7da89e422fab2670d43769d8260d04405f827795d4a8775e4425696e"}}