{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:Y3HNQ6RIESUD4AK3FSSW6UPJBT","short_pith_number":"pith:Y3HNQ6RI","canonical_record":{"source":{"id":"astro-ph/0105113","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2001-05-07T16:57:53Z","cross_cats_sorted":[],"title_canon_sha256":"8cbe5c2f0601aa5d92734bd762098f9334dae0a0d99f2f86bbdfb37a30a672e3","abstract_canon_sha256":"4a0942f9227f0f171e28cca5023d77b9f60549a45594e007d90a36a0515936ba"},"schema_version":"1.0"},"canonical_sha256":"c6ced87a2824a83e015b2ca56f51e90cfde41660dec86b2b69dff3f00a4a3dc6","source":{"kind":"arxiv","id":"astro-ph/0105113","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0105113","created_at":"2026-07-04T16:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0105113v1","created_at":"2026-07-04T16:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0105113","created_at":"2026-07-04T16:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"Y3HNQ6RIESUD","created_at":"2026-07-04T16:23:21Z"},{"alias_kind":"pith_short_16","alias_value":"Y3HNQ6RIESUD4AK3","created_at":"2026-07-04T16:23:21Z"},{"alias_kind":"pith_short_8","alias_value":"Y3HNQ6RI","created_at":"2026-07-04T16:23:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:Y3HNQ6RIESUD4AK3FSSW6UPJBT","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/0105113","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2001-05-07T16:57:53Z","cross_cats_sorted":[],"title_canon_sha256":"8cbe5c2f0601aa5d92734bd762098f9334dae0a0d99f2f86bbdfb37a30a672e3","abstract_canon_sha256":"4a0942f9227f0f171e28cca5023d77b9f60549a45594e007d90a36a0515936ba"},"schema_version":"1.0"},"canonical_sha256":"c6ced87a2824a83e015b2ca56f51e90cfde41660dec86b2b69dff3f00a4a3dc6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:23:21.376342Z","signature_b64":"AiVxtvIaTOVnSgwWwDxfEJZRpjoaPdeEnGPp0ocXXT8EhKkJqphkJ1z6i5Tj0v/FGkUnpGXlLltTMei67W+wBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6ced87a2824a83e015b2ca56f51e90cfde41660dec86b2b69dff3f00a4a3dc6","last_reissued_at":"2026-07-04T16:23:21.375839Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:23:21.375839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/0105113","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":"2026-07-04T16:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7oPhAqeEqoc4ITteEODU8LFlDSe5urATYQjG1XnHywSlyww7ZXlJSvajfO9wswQInrjBPXf94x+ZgLh7jBjiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T02:08:45.827531Z"},"content_sha256":"f74ce8e3cba998c17ee178bb8f2bad73a43090a8ce2af9dc9c87738477fe6054","schema_version":"1.0","event_id":"sha256:f74ce8e3cba998c17ee178bb8f2bad73a43090a8ce2af9dc9c87738477fe6054"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:Y3HNQ6RIESUD4AK3FSSW6UPJBT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An excursion set model of hierarchical clustering: Ellipsoidal collapse and the moving barrier","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Giuseppe Tormen (Padova), Ravi K. Sheth (Fermilab)","submitted_at":"2001-05-07T16:57:53Z","abstract_excerpt":"The excursion set approach allows one to estimate the abundance and spatial distribution of virialized dark matter haloes efficiently and accurately. The predictions of this approach depend on how the nonlinear processes of collapse and virialization are modelled. We present simple analytic approximations which allow us to compare the excursion set predictions associated with spherical and ellipsoidal collapse. In particular, we present formulae for the universal unconditional mass function of bound objects and the conditional mass function which describes the mass function of the progenitors "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0105113","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/astro-ph/0105113/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":"2026-07-04T16:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t8Oj0SeUdBka4CyD9x0D7/jxYOvEmiaBm4y8riYfz3Hvh8q+zZBUvRF4/MGxevqI1uhD2uraBj9ESE1sQ8MFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T02:08:45.828044Z"},"content_sha256":"730ab607f6a0dc77153c9534556bf39c00f0221cf738762f6723724bff2b768c","schema_version":"1.0","event_id":"sha256:730ab607f6a0dc77153c9534556bf39c00f0221cf738762f6723724bff2b768c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y3HNQ6RIESUD4AK3FSSW6UPJBT/bundle.json","state_url":"https://pith.science/pith/Y3HNQ6RIESUD4AK3FSSW6UPJBT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y3HNQ6RIESUD4AK3FSSW6UPJBT/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":"2026-08-02T02:08:45Z","links":{"resolver":"https://pith.science/pith/Y3HNQ6RIESUD4AK3FSSW6UPJBT","bundle":"https://pith.science/pith/Y3HNQ6RIESUD4AK3FSSW6UPJBT/bundle.json","state":"https://pith.science/pith/Y3HNQ6RIESUD4AK3FSSW6UPJBT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y3HNQ6RIESUD4AK3FSSW6UPJBT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:Y3HNQ6RIESUD4AK3FSSW6UPJBT","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":"4a0942f9227f0f171e28cca5023d77b9f60549a45594e007d90a36a0515936ba","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2001-05-07T16:57:53Z","title_canon_sha256":"8cbe5c2f0601aa5d92734bd762098f9334dae0a0d99f2f86bbdfb37a30a672e3"},"schema_version":"1.0","source":{"id":"astro-ph/0105113","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0105113","created_at":"2026-07-04T16:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0105113v1","created_at":"2026-07-04T16:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0105113","created_at":"2026-07-04T16:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"Y3HNQ6RIESUD","created_at":"2026-07-04T16:23:21Z"},{"alias_kind":"pith_short_16","alias_value":"Y3HNQ6RIESUD4AK3","created_at":"2026-07-04T16:23:21Z"},{"alias_kind":"pith_short_8","alias_value":"Y3HNQ6RI","created_at":"2026-07-04T16:23:21Z"}],"graph_snapshots":[{"event_id":"sha256:730ab607f6a0dc77153c9534556bf39c00f0221cf738762f6723724bff2b768c","target":"graph","created_at":"2026-07-04T16:23:21Z","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/astro-ph/0105113/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The excursion set approach allows one to estimate the abundance and spatial distribution of virialized dark matter haloes efficiently and accurately. The predictions of this approach depend on how the nonlinear processes of collapse and virialization are modelled. We present simple analytic approximations which allow us to compare the excursion set predictions associated with spherical and ellipsoidal collapse. In particular, we present formulae for the universal unconditional mass function of bound objects and the conditional mass function which describes the mass function of the progenitors ","authors_text":"Giuseppe Tormen (Padova), Ravi K. Sheth (Fermilab)","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2001-05-07T16:57:53Z","title":"An excursion set model of hierarchical clustering: Ellipsoidal collapse and the moving barrier"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0105113","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:f74ce8e3cba998c17ee178bb8f2bad73a43090a8ce2af9dc9c87738477fe6054","target":"record","created_at":"2026-07-04T16:23:21Z","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":"4a0942f9227f0f171e28cca5023d77b9f60549a45594e007d90a36a0515936ba","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2001-05-07T16:57:53Z","title_canon_sha256":"8cbe5c2f0601aa5d92734bd762098f9334dae0a0d99f2f86bbdfb37a30a672e3"},"schema_version":"1.0","source":{"id":"astro-ph/0105113","kind":"arxiv","version":1}},"canonical_sha256":"c6ced87a2824a83e015b2ca56f51e90cfde41660dec86b2b69dff3f00a4a3dc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6ced87a2824a83e015b2ca56f51e90cfde41660dec86b2b69dff3f00a4a3dc6","first_computed_at":"2026-07-04T16:23:21.375839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:23:21.375839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AiVxtvIaTOVnSgwWwDxfEJZRpjoaPdeEnGPp0ocXXT8EhKkJqphkJ1z6i5Tj0v/FGkUnpGXlLltTMei67W+wBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:23:21.376342Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0105113","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f74ce8e3cba998c17ee178bb8f2bad73a43090a8ce2af9dc9c87738477fe6054","sha256:730ab607f6a0dc77153c9534556bf39c00f0221cf738762f6723724bff2b768c"],"state_sha256":"e874e4a46ff170c563521565b333884c12eeec113a783df537489162ea77b908"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KYCxZx/SNhMSTRJpKYo9x6VG8BK5DJgghYdk5/FRNWFQa68RGPhxcmG82OQZSrnXfAUakT9gKhF+a7yI45LLBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-02T02:08:45.833146Z","bundle_sha256":"2efcb88e842515af33b041d709bada5d65504fda899ff20004359e519831d4a9"}}