{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:5JOQFXLIQ6ZB3GNF4DNMC3RLH6","short_pith_number":"pith:5JOQFXLI","canonical_record":{"source":{"id":"2508.07906","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-08-11T12:19:47Z","cross_cats_sorted":[],"title_canon_sha256":"41a0d3af77e1ba374073c7b402597177bd1dd94deaacd4f8c63f6411e8a187e8","abstract_canon_sha256":"7b668ef2f3f9d5475bb00b1f5a2ce956dbd0796c8331cf1da11815a8fbc4a961"},"schema_version":"1.0"},"canonical_sha256":"ea5d02dd6887b21d99a5e0dac16e2b3fb07339ae6c2b0cf8949461a9d4c4ed9a","source":{"kind":"arxiv","id":"2508.07906","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.07906","created_at":"2026-05-25T02:02:08Z"},{"alias_kind":"arxiv_version","alias_value":"2508.07906v2","created_at":"2026-05-25T02:02:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.07906","created_at":"2026-05-25T02:02:08Z"},{"alias_kind":"pith_short_12","alias_value":"5JOQFXLIQ6ZB","created_at":"2026-05-25T02:02:08Z"},{"alias_kind":"pith_short_16","alias_value":"5JOQFXLIQ6ZB3GNF","created_at":"2026-05-25T02:02:08Z"},{"alias_kind":"pith_short_8","alias_value":"5JOQFXLI","created_at":"2026-05-25T02:02:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:5JOQFXLIQ6ZB3GNF4DNMC3RLH6","target":"record","payload":{"canonical_record":{"source":{"id":"2508.07906","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-08-11T12:19:47Z","cross_cats_sorted":[],"title_canon_sha256":"41a0d3af77e1ba374073c7b402597177bd1dd94deaacd4f8c63f6411e8a187e8","abstract_canon_sha256":"7b668ef2f3f9d5475bb00b1f5a2ce956dbd0796c8331cf1da11815a8fbc4a961"},"schema_version":"1.0"},"canonical_sha256":"ea5d02dd6887b21d99a5e0dac16e2b3fb07339ae6c2b0cf8949461a9d4c4ed9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:02:08.258375Z","signature_b64":"bdcVTZU3KW2xrtzQwBDNNFqW/J5TB/EOpX/Uj74IvPtubsWONTIe9UnTNBfEmZdaaf/N967xrnw0W7ScG3lcBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea5d02dd6887b21d99a5e0dac16e2b3fb07339ae6c2b0cf8949461a9d4c4ed9a","last_reissued_at":"2026-05-25T02:02:08.257643Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:02:08.257643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.07906","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":"2026-05-25T02:02:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jfuM5Syu/6rGnWFynXzJhWwtAx4hgbvIrLN6tKMZ5rum+jdxQEma8OkntZL7VAb7sIaLtnC2aHzuhjL1FVKcBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T07:14:07.764625Z"},"content_sha256":"044ff524acd95370b4cfa90fceb8fb81eca6b76866f79ebcf7f251f303dd903e","schema_version":"1.0","event_id":"sha256:044ff524acd95370b4cfa90fceb8fb81eca6b76866f79ebcf7f251f303dd903e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:5JOQFXLIQ6ZB3GNF4DNMC3RLH6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Site Frequency Spectrum in stationary branching populations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Fran\\c{c}ois Delmas (CERMICS), Patrick Hoscheit (MaIAGE), Romain Abraham (IDP)","submitted_at":"2025-08-11T12:19:47Z","abstract_excerpt":"This paper explores the Site Frequency Spectrum (SFS) in stationary branching populations. We derive estimates for the SFS associated with a sample from a continuous-state branching process conditioned to never go extinct, utilizing a quadratic branching mechanism. The genealogy of such processes is represented by a real tree with a semi-infinite branch, and we compute the expectation of the SFS under the infinitely-many-sites assumption as the sample size approaches infinity. Additionally, we present a continuum version of the SFS as a random point measure on the positive real line and comput"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.07906","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.07906/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":"2026-05-25T02:02:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bLIxRw9SptGsjDBByfL/l/1hjrZrW6IYopCESW4JxM8RWUsHlv+BXQ/eGl2p20JrLUVp0EQlTzKdGvLemwKNCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T07:14:07.765002Z"},"content_sha256":"74794e2e3c49b0e19c034c32e256e7c5440c99295745d48cb94e01bea82c521d","schema_version":"1.0","event_id":"sha256:74794e2e3c49b0e19c034c32e256e7c5440c99295745d48cb94e01bea82c521d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5JOQFXLIQ6ZB3GNF4DNMC3RLH6/bundle.json","state_url":"https://pith.science/pith/5JOQFXLIQ6ZB3GNF4DNMC3RLH6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5JOQFXLIQ6ZB3GNF4DNMC3RLH6/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":"2026-06-22T07:14:07Z","links":{"resolver":"https://pith.science/pith/5JOQFXLIQ6ZB3GNF4DNMC3RLH6","bundle":"https://pith.science/pith/5JOQFXLIQ6ZB3GNF4DNMC3RLH6/bundle.json","state":"https://pith.science/pith/5JOQFXLIQ6ZB3GNF4DNMC3RLH6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5JOQFXLIQ6ZB3GNF4DNMC3RLH6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5JOQFXLIQ6ZB3GNF4DNMC3RLH6","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":"7b668ef2f3f9d5475bb00b1f5a2ce956dbd0796c8331cf1da11815a8fbc4a961","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-08-11T12:19:47Z","title_canon_sha256":"41a0d3af77e1ba374073c7b402597177bd1dd94deaacd4f8c63f6411e8a187e8"},"schema_version":"1.0","source":{"id":"2508.07906","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.07906","created_at":"2026-05-25T02:02:08Z"},{"alias_kind":"arxiv_version","alias_value":"2508.07906v2","created_at":"2026-05-25T02:02:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.07906","created_at":"2026-05-25T02:02:08Z"},{"alias_kind":"pith_short_12","alias_value":"5JOQFXLIQ6ZB","created_at":"2026-05-25T02:02:08Z"},{"alias_kind":"pith_short_16","alias_value":"5JOQFXLIQ6ZB3GNF","created_at":"2026-05-25T02:02:08Z"},{"alias_kind":"pith_short_8","alias_value":"5JOQFXLI","created_at":"2026-05-25T02:02:08Z"}],"graph_snapshots":[{"event_id":"sha256:74794e2e3c49b0e19c034c32e256e7c5440c99295745d48cb94e01bea82c521d","target":"graph","created_at":"2026-05-25T02:02:08Z","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/2508.07906/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper explores the Site Frequency Spectrum (SFS) in stationary branching populations. We derive estimates for the SFS associated with a sample from a continuous-state branching process conditioned to never go extinct, utilizing a quadratic branching mechanism. The genealogy of such processes is represented by a real tree with a semi-infinite branch, and we compute the expectation of the SFS under the infinitely-many-sites assumption as the sample size approaches infinity. Additionally, we present a continuum version of the SFS as a random point measure on the positive real line and comput","authors_text":"Jean-Fran\\c{c}ois Delmas (CERMICS), Patrick Hoscheit (MaIAGE), Romain Abraham (IDP)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-08-11T12:19:47Z","title":"Site Frequency Spectrum in stationary branching populations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.07906","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":"sha256:044ff524acd95370b4cfa90fceb8fb81eca6b76866f79ebcf7f251f303dd903e","target":"record","created_at":"2026-05-25T02:02:08Z","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":"7b668ef2f3f9d5475bb00b1f5a2ce956dbd0796c8331cf1da11815a8fbc4a961","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-08-11T12:19:47Z","title_canon_sha256":"41a0d3af77e1ba374073c7b402597177bd1dd94deaacd4f8c63f6411e8a187e8"},"schema_version":"1.0","source":{"id":"2508.07906","kind":"arxiv","version":2}},"canonical_sha256":"ea5d02dd6887b21d99a5e0dac16e2b3fb07339ae6c2b0cf8949461a9d4c4ed9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea5d02dd6887b21d99a5e0dac16e2b3fb07339ae6c2b0cf8949461a9d4c4ed9a","first_computed_at":"2026-05-25T02:02:08.257643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:02:08.257643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bdcVTZU3KW2xrtzQwBDNNFqW/J5TB/EOpX/Uj74IvPtubsWONTIe9UnTNBfEmZdaaf/N967xrnw0W7ScG3lcBg==","signature_status":"signed_v1","signed_at":"2026-05-25T02:02:08.258375Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.07906","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:044ff524acd95370b4cfa90fceb8fb81eca6b76866f79ebcf7f251f303dd903e","sha256:74794e2e3c49b0e19c034c32e256e7c5440c99295745d48cb94e01bea82c521d"],"state_sha256":"61b1487b0544e9f6b05e8407904e6402a5c35d1d4096c9c7b48e2a005583fb0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XsgmE42gJK8L0J/UXBBmUSXp4DHpeIy+CCo8d7AZK7EOBhjvcW0BzY/57spuisPZ2HcwkNsSYcbutRv9K4liDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T07:14:07.767055Z","bundle_sha256":"74b7238a81492269526b139072ed4eaed4685765ebf924e0e6e1d790736f3630"}}