{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:TQXVIXPL6RDOAHOJAKJWOCJIF2","short_pith_number":"pith:TQXVIXPL","canonical_record":{"source":{"id":"2409.02780","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2024-09-04T14:57:00Z","cross_cats_sorted":[],"title_canon_sha256":"cc39885f8cd7990e753d8131d330191fffb5c43f28c6cd43cd0f56e15fb8cadd","abstract_canon_sha256":"368a508d2179817a43ebea8d611d9e40a69eff8d8432d95406370ccedb0241d5"},"schema_version":"1.0"},"canonical_sha256":"9c2f545debf446e01dc902936709282eaf791924b1655a64fefb3282a4089e30","source":{"kind":"arxiv","id":"2409.02780","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.02780","created_at":"2026-07-05T09:03:10Z"},{"alias_kind":"arxiv_version","alias_value":"2409.02780v1","created_at":"2026-07-05T09:03:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.02780","created_at":"2026-07-05T09:03:10Z"},{"alias_kind":"pith_short_12","alias_value":"TQXVIXPL6RDO","created_at":"2026-07-05T09:03:10Z"},{"alias_kind":"pith_short_16","alias_value":"TQXVIXPL6RDOAHOJ","created_at":"2026-07-05T09:03:10Z"},{"alias_kind":"pith_short_8","alias_value":"TQXVIXPL","created_at":"2026-07-05T09:03:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:TQXVIXPL6RDOAHOJAKJWOCJIF2","target":"record","payload":{"canonical_record":{"source":{"id":"2409.02780","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2024-09-04T14:57:00Z","cross_cats_sorted":[],"title_canon_sha256":"cc39885f8cd7990e753d8131d330191fffb5c43f28c6cd43cd0f56e15fb8cadd","abstract_canon_sha256":"368a508d2179817a43ebea8d611d9e40a69eff8d8432d95406370ccedb0241d5"},"schema_version":"1.0"},"canonical_sha256":"9c2f545debf446e01dc902936709282eaf791924b1655a64fefb3282a4089e30","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:03:10.106911Z","signature_b64":"4W80/ggsUltbsEwA4Xn+7lvTeYUD6fyubcSJVYTuNKfsb/rpAqSJXQ5YWhU7WxyHqIHMmhiBesl2iQpRlB7QBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c2f545debf446e01dc902936709282eaf791924b1655a64fefb3282a4089e30","last_reissued_at":"2026-07-05T09:03:10.106432Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:03:10.106432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.02780","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":"2026-07-05T09:03:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8vwCXcHRiAXK1AeXtWeJKbGa2RXQrCntN+c3NkRTMjRaJJ//M3mxS+CL+Fl6lhD3jeFvBVIcZKN9P/Wv1yrWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-28T05:00:09.814726Z"},"content_sha256":"1e67a01528ef4dd96f65039a02a0b8a60cd459bea55489ecaaa5ce1bef0acc0c","schema_version":"1.0","event_id":"sha256:1e67a01528ef4dd96f65039a02a0b8a60cd459bea55489ecaaa5ce1bef0acc0c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:TQXVIXPL6RDOAHOJAKJWOCJIF2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How empty are the voids?","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Anton N. Baushev","submitted_at":"2024-09-04T14:57:00Z","abstract_excerpt":"We find an analytical solution for the minimal matter density of a void, its central density. It turns out that the voids are not so empty: most of the voids have the central underdensity $\\Delta_c \\sim -50\\%$ (which means that the matter density in their centers is only two times lower than in the Universe on average). For small voids (of radius $R_0\\simeq 5-10$~{Mpc}), the underdensity can be significantly greater, but the number of voids decreases rapidly with increasing of $|\\Delta_c|$ over $50\\%$, and voids with $\\Delta_c < -80\\%$ are practically absent. The large voids ($R_0\\ge 40$~{Mpc}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.02780","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/2409.02780/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":"2026-07-05T09:03:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hQQBtMILKvjv1vfuScHRocsI2jp5mu2FYRi2eBUHiBfkzLSiEYh0+i9vbX7tZdM6p9YEaMjGFtxyU68WInFCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-28T05:00:09.815104Z"},"content_sha256":"ed04a2de318afd2894824aa9b16b7ad5160bb4b8d4b10490305ac9c4058b61a3","schema_version":"1.0","event_id":"sha256:ed04a2de318afd2894824aa9b16b7ad5160bb4b8d4b10490305ac9c4058b61a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQXVIXPL6RDOAHOJAKJWOCJIF2/bundle.json","state_url":"https://pith.science/pith/TQXVIXPL6RDOAHOJAKJWOCJIF2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQXVIXPL6RDOAHOJAKJWOCJIF2/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":"2026-07-28T05:00:09Z","links":{"resolver":"https://pith.science/pith/TQXVIXPL6RDOAHOJAKJWOCJIF2","bundle":"https://pith.science/pith/TQXVIXPL6RDOAHOJAKJWOCJIF2/bundle.json","state":"https://pith.science/pith/TQXVIXPL6RDOAHOJAKJWOCJIF2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQXVIXPL6RDOAHOJAKJWOCJIF2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TQXVIXPL6RDOAHOJAKJWOCJIF2","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":"368a508d2179817a43ebea8d611d9e40a69eff8d8432d95406370ccedb0241d5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2024-09-04T14:57:00Z","title_canon_sha256":"cc39885f8cd7990e753d8131d330191fffb5c43f28c6cd43cd0f56e15fb8cadd"},"schema_version":"1.0","source":{"id":"2409.02780","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.02780","created_at":"2026-07-05T09:03:10Z"},{"alias_kind":"arxiv_version","alias_value":"2409.02780v1","created_at":"2026-07-05T09:03:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.02780","created_at":"2026-07-05T09:03:10Z"},{"alias_kind":"pith_short_12","alias_value":"TQXVIXPL6RDO","created_at":"2026-07-05T09:03:10Z"},{"alias_kind":"pith_short_16","alias_value":"TQXVIXPL6RDOAHOJ","created_at":"2026-07-05T09:03:10Z"},{"alias_kind":"pith_short_8","alias_value":"TQXVIXPL","created_at":"2026-07-05T09:03:10Z"}],"graph_snapshots":[{"event_id":"sha256:ed04a2de318afd2894824aa9b16b7ad5160bb4b8d4b10490305ac9c4058b61a3","target":"graph","created_at":"2026-07-05T09:03:10Z","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/2409.02780/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We find an analytical solution for the minimal matter density of a void, its central density. It turns out that the voids are not so empty: most of the voids have the central underdensity $\\Delta_c \\sim -50\\%$ (which means that the matter density in their centers is only two times lower than in the Universe on average). For small voids (of radius $R_0\\simeq 5-10$~{Mpc}), the underdensity can be significantly greater, but the number of voids decreases rapidly with increasing of $|\\Delta_c|$ over $50\\%$, and voids with $\\Delta_c < -80\\%$ are practically absent. The large voids ($R_0\\ge 40$~{Mpc}","authors_text":"Anton N. Baushev","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2024-09-04T14:57:00Z","title":"How empty are the voids?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.02780","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":"sha256:1e67a01528ef4dd96f65039a02a0b8a60cd459bea55489ecaaa5ce1bef0acc0c","target":"record","created_at":"2026-07-05T09:03:10Z","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":"368a508d2179817a43ebea8d611d9e40a69eff8d8432d95406370ccedb0241d5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2024-09-04T14:57:00Z","title_canon_sha256":"cc39885f8cd7990e753d8131d330191fffb5c43f28c6cd43cd0f56e15fb8cadd"},"schema_version":"1.0","source":{"id":"2409.02780","kind":"arxiv","version":1}},"canonical_sha256":"9c2f545debf446e01dc902936709282eaf791924b1655a64fefb3282a4089e30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c2f545debf446e01dc902936709282eaf791924b1655a64fefb3282a4089e30","first_computed_at":"2026-07-05T09:03:10.106432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:03:10.106432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4W80/ggsUltbsEwA4Xn+7lvTeYUD6fyubcSJVYTuNKfsb/rpAqSJXQ5YWhU7WxyHqIHMmhiBesl2iQpRlB7QBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:03:10.106911Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.02780","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e67a01528ef4dd96f65039a02a0b8a60cd459bea55489ecaaa5ce1bef0acc0c","sha256:ed04a2de318afd2894824aa9b16b7ad5160bb4b8d4b10490305ac9c4058b61a3"],"state_sha256":"c52d2a3d0d7dd019edfb3961e3d3256bf5a7084f234b09a9f6aa10d91931bd5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jopfsXR3DKFcO8oqCw6CafqpxEtHcxsVwDAeNKBb2AwjgOrJgo+cVjjiisdnYstAkaSNHApf+DsivuKeSdiyCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-28T05:00:09.817237Z","bundle_sha256":"db409a837f0dffb25f98f447f6b9db8c09c3c5dc67b027c652186ee8332364ca"}}