{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BV77WXTKA45LOCW3AHBX47SGNF","short_pith_number":"pith:BV77WXTK","canonical_record":{"source":{"id":"1201.1382","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-01-06T09:58:52Z","cross_cats_sorted":[],"title_canon_sha256":"54a58a96db82391ab271ff19b39483b87c5c0ef43525d9f95b0aff0933642d6d","abstract_canon_sha256":"188bfe40c3a1a22206ff71a07a7df8c7c0ed0cc3106c5a90a9eb4e2d552ac1f2"},"schema_version":"1.0"},"canonical_sha256":"0d7ffb5e6a073ab70adb01c37e7e466960f2a49d5faba8fdd6454d7c3f45f512","source":{"kind":"arxiv","id":"1201.1382","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1382","created_at":"2026-05-18T01:58:54Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1382v2","created_at":"2026-05-18T01:58:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1382","created_at":"2026-05-18T01:58:54Z"},{"alias_kind":"pith_short_12","alias_value":"BV77WXTKA45L","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BV77WXTKA45LOCW3","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BV77WXTK","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BV77WXTKA45LOCW3AHBX47SGNF","target":"record","payload":{"canonical_record":{"source":{"id":"1201.1382","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-01-06T09:58:52Z","cross_cats_sorted":[],"title_canon_sha256":"54a58a96db82391ab271ff19b39483b87c5c0ef43525d9f95b0aff0933642d6d","abstract_canon_sha256":"188bfe40c3a1a22206ff71a07a7df8c7c0ed0cc3106c5a90a9eb4e2d552ac1f2"},"schema_version":"1.0"},"canonical_sha256":"0d7ffb5e6a073ab70adb01c37e7e466960f2a49d5faba8fdd6454d7c3f45f512","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:54.982212Z","signature_b64":"Ib9ljtjytRx5iXLEEe95grPMlczEgqhPnyNJBHwNKI0q3knlu5MNfMAa+fz9kY5GvHefuTgjRxLN9fwF+LffAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d7ffb5e6a073ab70adb01c37e7e466960f2a49d5faba8fdd6454d7c3f45f512","last_reissued_at":"2026-05-18T01:58:54.981412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:54.981412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.1382","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":"2026-05-18T01:58:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4kFF7dunuNLM/G7z0DubTLygung67nKDJwIIvTNSLGGeNylVWnsNsxvX4nWLoznGc+eNDHu69hUYv+Ho2efGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:19:52.317371Z"},"content_sha256":"d000cd51a917a05a7414597a8d4b9eec332da72bbc924d73633b75307a96a2b9","schema_version":"1.0","event_id":"sha256:d000cd51a917a05a7414597a8d4b9eec332da72bbc924d73633b75307a96a2b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BV77WXTKA45LOCW3AHBX47SGNF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Analytic Formula for the Supercluster Mass Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"2), (2) Seoul National University), Jounghun Lee (2) ((1) UMass at Amherst, Seunghwan Lim (1","submitted_at":"2012-01-06T09:58:52Z","abstract_excerpt":"We present an analytic formula for the supercluster mass function which is constructed by modifying the extended Zel'dovich model for the halo mass function. The formula has two characteristic parameters whose best-fit values are determined by fitting to the numerical results from N-body simulations for the standard LambdaCDM cosmology. The parameters are found to be independent of redshifts and robust against variation of the key cosmological parameters. Under the assumption that the same formula for the supercluster mass function is valid for non-standard cosmological models, we show that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1382","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":""},"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":"2026-05-18T01:58:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BVflKf4AtzqVSOL1VNeDbMKZOK+KgB2lS085sNMcNq29jY7JMmTGcsrX/EaoXZzNEgs2AnXTnMa6gBEpGWS3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:19:52.318033Z"},"content_sha256":"4e363d13155ca9b49303e3e2d92d055a3481defcfadffa46c173eaf9f60a8293","schema_version":"1.0","event_id":"sha256:4e363d13155ca9b49303e3e2d92d055a3481defcfadffa46c173eaf9f60a8293"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BV77WXTKA45LOCW3AHBX47SGNF/bundle.json","state_url":"https://pith.science/pith/BV77WXTKA45LOCW3AHBX47SGNF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BV77WXTKA45LOCW3AHBX47SGNF/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":"2026-05-26T12:19:52Z","links":{"resolver":"https://pith.science/pith/BV77WXTKA45LOCW3AHBX47SGNF","bundle":"https://pith.science/pith/BV77WXTKA45LOCW3AHBX47SGNF/bundle.json","state":"https://pith.science/pith/BV77WXTKA45LOCW3AHBX47SGNF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BV77WXTKA45LOCW3AHBX47SGNF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BV77WXTKA45LOCW3AHBX47SGNF","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":"188bfe40c3a1a22206ff71a07a7df8c7c0ed0cc3106c5a90a9eb4e2d552ac1f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-01-06T09:58:52Z","title_canon_sha256":"54a58a96db82391ab271ff19b39483b87c5c0ef43525d9f95b0aff0933642d6d"},"schema_version":"1.0","source":{"id":"1201.1382","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1382","created_at":"2026-05-18T01:58:54Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1382v2","created_at":"2026-05-18T01:58:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1382","created_at":"2026-05-18T01:58:54Z"},{"alias_kind":"pith_short_12","alias_value":"BV77WXTKA45L","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BV77WXTKA45LOCW3","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BV77WXTK","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:4e363d13155ca9b49303e3e2d92d055a3481defcfadffa46c173eaf9f60a8293","target":"graph","created_at":"2026-05-18T01:58:54Z","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"},"paper":{"abstract_excerpt":"We present an analytic formula for the supercluster mass function which is constructed by modifying the extended Zel'dovich model for the halo mass function. The formula has two characteristic parameters whose best-fit values are determined by fitting to the numerical results from N-body simulations for the standard LambdaCDM cosmology. The parameters are found to be independent of redshifts and robust against variation of the key cosmological parameters. Under the assumption that the same formula for the supercluster mass function is valid for non-standard cosmological models, we show that th","authors_text":"2), (2) Seoul National University), Jounghun Lee (2) ((1) UMass at Amherst, Seunghwan Lim (1","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-01-06T09:58:52Z","title":"An Analytic Formula for the Supercluster Mass Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1382","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:d000cd51a917a05a7414597a8d4b9eec332da72bbc924d73633b75307a96a2b9","target":"record","created_at":"2026-05-18T01:58:54Z","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":"188bfe40c3a1a22206ff71a07a7df8c7c0ed0cc3106c5a90a9eb4e2d552ac1f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-01-06T09:58:52Z","title_canon_sha256":"54a58a96db82391ab271ff19b39483b87c5c0ef43525d9f95b0aff0933642d6d"},"schema_version":"1.0","source":{"id":"1201.1382","kind":"arxiv","version":2}},"canonical_sha256":"0d7ffb5e6a073ab70adb01c37e7e466960f2a49d5faba8fdd6454d7c3f45f512","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d7ffb5e6a073ab70adb01c37e7e466960f2a49d5faba8fdd6454d7c3f45f512","first_computed_at":"2026-05-18T01:58:54.981412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:54.981412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ib9ljtjytRx5iXLEEe95grPMlczEgqhPnyNJBHwNKI0q3knlu5MNfMAa+fz9kY5GvHefuTgjRxLN9fwF+LffAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:54.982212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1382","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d000cd51a917a05a7414597a8d4b9eec332da72bbc924d73633b75307a96a2b9","sha256:4e363d13155ca9b49303e3e2d92d055a3481defcfadffa46c173eaf9f60a8293"],"state_sha256":"5c521566ac409034c0eb682e672661dbe87dd72c4374b4139ded5207ead18904"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"klHWiQns99v6MqdteKQLCeRhGe+mbu/QY9XKoaWSZJjSuGDaQSZK6fzppyExSc/H/I6mFEZo/XxDSer+2GckDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:19:52.321423Z","bundle_sha256":"e7b511d57e6c38784ff5495cf5b659d590aeb3a312f8cb49423d5abdefc199ce"}}