{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PV7F3VKSX3Q6I4JR2WEUZRF3I4","short_pith_number":"pith:PV7F3VKS","canonical_record":{"source":{"id":"1210.7012","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-25T22:17:29Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"215972362c9785dfc32033a8711d2b262860792da52189a8d0f092e1b3485785","abstract_canon_sha256":"0f3d46a536930116709b8ac4ed1c46df452980f92328a63b2cd40c5e411cb660"},"schema_version":"1.0"},"canonical_sha256":"7d7e5dd552bee1e47131d5894cc4bb4722ffa6db9eb62a1ae453a4aaaaa9027b","source":{"kind":"arxiv","id":"1210.7012","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7012","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7012v2","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7012","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"pith_short_12","alias_value":"PV7F3VKSX3Q6","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PV7F3VKSX3Q6I4JR","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PV7F3VKS","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PV7F3VKSX3Q6I4JR2WEUZRF3I4","target":"record","payload":{"canonical_record":{"source":{"id":"1210.7012","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-25T22:17:29Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"215972362c9785dfc32033a8711d2b262860792da52189a8d0f092e1b3485785","abstract_canon_sha256":"0f3d46a536930116709b8ac4ed1c46df452980f92328a63b2cd40c5e411cb660"},"schema_version":"1.0"},"canonical_sha256":"7d7e5dd552bee1e47131d5894cc4bb4722ffa6db9eb62a1ae453a4aaaaa9027b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:27.960808Z","signature_b64":"Vw33u07gxZpkxsfpOuoc4cwTcOrx0lh7N5E3n4QUJa5JfO5CsL0CcvOx1UF5rPIvaw498MzB9Lu2R7AQEBC/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d7e5dd552bee1e47131d5894cc4bb4722ffa6db9eb62a1ae453a4aaaaa9027b","last_reissued_at":"2026-05-18T03:39:27.960271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:27.960271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.7012","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":"2026-05-18T03:39:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zTmwpqilYhHW45j1tL6L7R7POXRIOtgyadFUeiQBAm/rW1iZgRsQyJyczXfpYKXyY8ELPQ+6+lZyVsydzIyVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:32:17.913455Z"},"content_sha256":"ca2dc257100790bfc83cffddd9aa18c594b930a037e29e3e3d45272c930197a8","schema_version":"1.0","event_id":"sha256:ca2dc257100790bfc83cffddd9aa18c594b930a037e29e3e3d45272c930197a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PV7F3VKSX3Q6I4JR2WEUZRF3I4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A central limit theorem for projections of the cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Grigoris Paouris, Joel Zinn, Peter Pivovarov","submitted_at":"2012-10-25T22:17:29Z","abstract_excerpt":"We prove a central limit theorem for the volume of projections of the N-cube onto a random subspace of dimension n, when n is fixed and N tends to infinity. Randomness in this case is with respect to the Haar measure on the Grassmannian manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7012","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":"2026-05-18T03:39:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kLDh0cPiRYQjREd+9Lin0nfTvQ5ozPzC6AKj3V811w1Q/wDbd7vDzVnNmk8FTHlTMIeI1r5WwskZmbcWKC/SAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:32:17.914085Z"},"content_sha256":"64c30d0069fce0bdc4cc5d20750a819be1c5ec1635064b1d4141f7f444072e17","schema_version":"1.0","event_id":"sha256:64c30d0069fce0bdc4cc5d20750a819be1c5ec1635064b1d4141f7f444072e17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PV7F3VKSX3Q6I4JR2WEUZRF3I4/bundle.json","state_url":"https://pith.science/pith/PV7F3VKSX3Q6I4JR2WEUZRF3I4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PV7F3VKSX3Q6I4JR2WEUZRF3I4/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":"2026-06-04T04:32:17Z","links":{"resolver":"https://pith.science/pith/PV7F3VKSX3Q6I4JR2WEUZRF3I4","bundle":"https://pith.science/pith/PV7F3VKSX3Q6I4JR2WEUZRF3I4/bundle.json","state":"https://pith.science/pith/PV7F3VKSX3Q6I4JR2WEUZRF3I4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PV7F3VKSX3Q6I4JR2WEUZRF3I4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PV7F3VKSX3Q6I4JR2WEUZRF3I4","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":"0f3d46a536930116709b8ac4ed1c46df452980f92328a63b2cd40c5e411cb660","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-25T22:17:29Z","title_canon_sha256":"215972362c9785dfc32033a8711d2b262860792da52189a8d0f092e1b3485785"},"schema_version":"1.0","source":{"id":"1210.7012","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7012","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7012v2","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7012","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"pith_short_12","alias_value":"PV7F3VKSX3Q6","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PV7F3VKSX3Q6I4JR","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PV7F3VKS","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:64c30d0069fce0bdc4cc5d20750a819be1c5ec1635064b1d4141f7f444072e17","target":"graph","created_at":"2026-05-18T03:39:27Z","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 prove a central limit theorem for the volume of projections of the N-cube onto a random subspace of dimension n, when n is fixed and N tends to infinity. Randomness in this case is with respect to the Haar measure on the Grassmannian manifold.","authors_text":"Grigoris Paouris, Joel Zinn, Peter Pivovarov","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-25T22:17:29Z","title":"A central limit theorem for projections of the cube"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7012","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:ca2dc257100790bfc83cffddd9aa18c594b930a037e29e3e3d45272c930197a8","target":"record","created_at":"2026-05-18T03:39:27Z","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":"0f3d46a536930116709b8ac4ed1c46df452980f92328a63b2cd40c5e411cb660","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-10-25T22:17:29Z","title_canon_sha256":"215972362c9785dfc32033a8711d2b262860792da52189a8d0f092e1b3485785"},"schema_version":"1.0","source":{"id":"1210.7012","kind":"arxiv","version":2}},"canonical_sha256":"7d7e5dd552bee1e47131d5894cc4bb4722ffa6db9eb62a1ae453a4aaaaa9027b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d7e5dd552bee1e47131d5894cc4bb4722ffa6db9eb62a1ae453a4aaaaa9027b","first_computed_at":"2026-05-18T03:39:27.960271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:27.960271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vw33u07gxZpkxsfpOuoc4cwTcOrx0lh7N5E3n4QUJa5JfO5CsL0CcvOx1UF5rPIvaw498MzB9Lu2R7AQEBC/AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:27.960808Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.7012","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca2dc257100790bfc83cffddd9aa18c594b930a037e29e3e3d45272c930197a8","sha256:64c30d0069fce0bdc4cc5d20750a819be1c5ec1635064b1d4141f7f444072e17"],"state_sha256":"a20bdefb2271f41423cb9ecbbd374a7fd9055b5f2f6e43ba239e79faf55d3190"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kSZ0lwv9BV5/qv0bX9DSNeZHhhTxK14mZRXXYjN9W/Ph2dGMdLlayz7vvZC05J6Ri6lKhsirdXW6Sd4Jl433CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:32:17.917130Z","bundle_sha256":"70dce643120cb41edc18ff6baec591d8a2457040fe7bd689b764ccfc0826ada1"}}