{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:LF6AGDGN25XTG3OBRJC7DQ3KTG","short_pith_number":"pith:LF6AGDGN","canonical_record":{"source":{"id":"2605.28943","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-05-27T18:00:04Z","cross_cats_sorted":[],"title_canon_sha256":"8a4529df7de1c80ae0a204272579c79d932a842251435258226dfe9626a3a8c9","abstract_canon_sha256":"a34c6dcf4a7260e9ce4c2b27b2c55e421d82c430c0e4479ff814679482a97ffb"},"schema_version":"1.0"},"canonical_sha256":"597c030ccdd76f336dc18a45f1c36a998d55b1d801f92452df30025c7f34801c","source":{"kind":"arxiv","id":"2605.28943","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.28943","created_at":"2026-05-29T00:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"2605.28943v1","created_at":"2026-05-29T00:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.28943","created_at":"2026-05-29T00:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"LF6AGDGN25XT","created_at":"2026-05-29T00:04:17Z"},{"alias_kind":"pith_short_16","alias_value":"LF6AGDGN25XTG3OB","created_at":"2026-05-29T00:04:17Z"},{"alias_kind":"pith_short_8","alias_value":"LF6AGDGN","created_at":"2026-05-29T00:04:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:LF6AGDGN25XTG3OBRJC7DQ3KTG","target":"record","payload":{"canonical_record":{"source":{"id":"2605.28943","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-05-27T18:00:04Z","cross_cats_sorted":[],"title_canon_sha256":"8a4529df7de1c80ae0a204272579c79d932a842251435258226dfe9626a3a8c9","abstract_canon_sha256":"a34c6dcf4a7260e9ce4c2b27b2c55e421d82c430c0e4479ff814679482a97ffb"},"schema_version":"1.0"},"canonical_sha256":"597c030ccdd76f336dc18a45f1c36a998d55b1d801f92452df30025c7f34801c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T00:04:17.446105Z","signature_b64":"f2EM9E6AcgJUZRx/Yg4c/BbzdaEVVO1tVgw6XveoHBvOUs1P74kg2Jiosn0IGs4/4sOds0a+8yRWWemcpW52Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"597c030ccdd76f336dc18a45f1c36a998d55b1d801f92452df30025c7f34801c","last_reissued_at":"2026-05-29T00:04:17.445571Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T00:04:17.445571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.28943","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":"2026-05-29T00:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"brGaK6Ay7pLW8khLaGFDMXJnc6b5FtZaAjNIx6prnxplF0HzJjsY/v7V1calFhAPApETpJzjjcvjJe8kLXlpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T23:28:07.411617Z"},"content_sha256":"6c2d9250d38db4443bdf34670e4e27a01302c75bbcb37a7421e809a86314a07e","schema_version":"1.0","event_id":"sha256:6c2d9250d38db4443bdf34670e4e27a01302c75bbcb37a7421e809a86314a07e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:LF6AGDGN25XTG3OBRJC7DQ3KTG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dominated-Convergence Failure in Cosmological Perturbation Theory and a Numerical Foundation for BBGKY+ZA","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Svetlin V. Tassev","submitted_at":"2026-05-27T18:00:04Z","abstract_excerpt":"A common ingredient in cosmological perturbation theory (PT) is the expansion of the dark matter overdensity $\\delta$ in the Lagrangian displacement $s$, which amounts to enforcing mass conservation perturbatively. In Eulerian PT (EPT), that expansion occurs already at the level of the continuity equation; in Lagrangian PT (LPT) it is done in the Poisson equation. We show that the resulting perturbative solutions for $\\delta$ can diverge not because of the expansion in $s$ per se, but because of an exchange of an infinite sum with a Fourier integral that violates the conditions of Lebesgue's d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28943","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/2605.28943/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":"2026-05-29T00:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iLISnj7fbgMRSq7Nc1hhsRFE+0kTeRyyoRVfvmqUsOur41NUi7S6tOAlb+q7f6SraZVPQ+NFGvh6pFOcrOazAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T23:28:07.411978Z"},"content_sha256":"2f38ec35912d9c03cf83a3cb7e63e3095e820e4ca130f0543f51a5e7b79dc32c","schema_version":"1.0","event_id":"sha256:2f38ec35912d9c03cf83a3cb7e63e3095e820e4ca130f0543f51a5e7b79dc32c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LF6AGDGN25XTG3OBRJC7DQ3KTG/bundle.json","state_url":"https://pith.science/pith/LF6AGDGN25XTG3OBRJC7DQ3KTG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LF6AGDGN25XTG3OBRJC7DQ3KTG/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":"2026-06-29T23:28:07Z","links":{"resolver":"https://pith.science/pith/LF6AGDGN25XTG3OBRJC7DQ3KTG","bundle":"https://pith.science/pith/LF6AGDGN25XTG3OBRJC7DQ3KTG/bundle.json","state":"https://pith.science/pith/LF6AGDGN25XTG3OBRJC7DQ3KTG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LF6AGDGN25XTG3OBRJC7DQ3KTG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LF6AGDGN25XTG3OBRJC7DQ3KTG","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":"a34c6dcf4a7260e9ce4c2b27b2c55e421d82c430c0e4479ff814679482a97ffb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-05-27T18:00:04Z","title_canon_sha256":"8a4529df7de1c80ae0a204272579c79d932a842251435258226dfe9626a3a8c9"},"schema_version":"1.0","source":{"id":"2605.28943","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.28943","created_at":"2026-05-29T00:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"2605.28943v1","created_at":"2026-05-29T00:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.28943","created_at":"2026-05-29T00:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"LF6AGDGN25XT","created_at":"2026-05-29T00:04:17Z"},{"alias_kind":"pith_short_16","alias_value":"LF6AGDGN25XTG3OB","created_at":"2026-05-29T00:04:17Z"},{"alias_kind":"pith_short_8","alias_value":"LF6AGDGN","created_at":"2026-05-29T00:04:17Z"}],"graph_snapshots":[{"event_id":"sha256:2f38ec35912d9c03cf83a3cb7e63e3095e820e4ca130f0543f51a5e7b79dc32c","target":"graph","created_at":"2026-05-29T00:04:17Z","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/2605.28943/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A common ingredient in cosmological perturbation theory (PT) is the expansion of the dark matter overdensity $\\delta$ in the Lagrangian displacement $s$, which amounts to enforcing mass conservation perturbatively. In Eulerian PT (EPT), that expansion occurs already at the level of the continuity equation; in Lagrangian PT (LPT) it is done in the Poisson equation. We show that the resulting perturbative solutions for $\\delta$ can diverge not because of the expansion in $s$ per se, but because of an exchange of an infinite sum with a Fourier integral that violates the conditions of Lebesgue's d","authors_text":"Svetlin V. Tassev","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-05-27T18:00:04Z","title":"Dominated-Convergence Failure in Cosmological Perturbation Theory and a Numerical Foundation for BBGKY+ZA"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28943","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":"sha256:6c2d9250d38db4443bdf34670e4e27a01302c75bbcb37a7421e809a86314a07e","target":"record","created_at":"2026-05-29T00:04:17Z","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":"a34c6dcf4a7260e9ce4c2b27b2c55e421d82c430c0e4479ff814679482a97ffb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-05-27T18:00:04Z","title_canon_sha256":"8a4529df7de1c80ae0a204272579c79d932a842251435258226dfe9626a3a8c9"},"schema_version":"1.0","source":{"id":"2605.28943","kind":"arxiv","version":1}},"canonical_sha256":"597c030ccdd76f336dc18a45f1c36a998d55b1d801f92452df30025c7f34801c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"597c030ccdd76f336dc18a45f1c36a998d55b1d801f92452df30025c7f34801c","first_computed_at":"2026-05-29T00:04:17.445571Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T00:04:17.445571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f2EM9E6AcgJUZRx/Yg4c/BbzdaEVVO1tVgw6XveoHBvOUs1P74kg2Jiosn0IGs4/4sOds0a+8yRWWemcpW52Dg==","signature_status":"signed_v1","signed_at":"2026-05-29T00:04:17.446105Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.28943","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c2d9250d38db4443bdf34670e4e27a01302c75bbcb37a7421e809a86314a07e","sha256:2f38ec35912d9c03cf83a3cb7e63e3095e820e4ca130f0543f51a5e7b79dc32c"],"state_sha256":"37727a1cfd1eb5ad87d39669408fdaa8724a60fdefb3d75dce1bc3f3335a9976"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"74X4A5NQp8jdphlVWmlWb4J/upbjWdQGB/KaqIqw1FAJsfCm+/YGR76SqqJovUvPDeUClBt8/OrFlKIUNf4BCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T23:28:07.413967Z","bundle_sha256":"39d07c680b8e3b3724fbed43f344c7e9056ff520996e378a88efc113b7d6c809"}}