{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:VOFGPTOIYDJ7LZSQAGUZDQH2IZ","short_pith_number":"pith:VOFGPTOI","canonical_record":{"source":{"id":"1310.4266","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T04:29:01Z","cross_cats_sorted":[],"title_canon_sha256":"01ce52c0dcb3d545a98bde6e2b29da3dda41c43e89f6ac19fb275a960f469856","abstract_canon_sha256":"0f1136b4d28de1ba3e6c7c13630cb59db51d18e68d0c80a87cc1c15b3c10f6ac"},"schema_version":"1.0"},"canonical_sha256":"ab8a67cdc8c0d3f5e65001a991c0fa4644f5fbe0826413eeeb0a9e197d4d78e1","source":{"kind":"arxiv","id":"1310.4266","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4266","created_at":"2026-05-18T02:30:32Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4266v1","created_at":"2026-05-18T02:30:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4266","created_at":"2026-05-18T02:30:32Z"},{"alias_kind":"pith_short_12","alias_value":"VOFGPTOIYDJ7","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VOFGPTOIYDJ7LZSQ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VOFGPTOI","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:VOFGPTOIYDJ7LZSQAGUZDQH2IZ","target":"record","payload":{"canonical_record":{"source":{"id":"1310.4266","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T04:29:01Z","cross_cats_sorted":[],"title_canon_sha256":"01ce52c0dcb3d545a98bde6e2b29da3dda41c43e89f6ac19fb275a960f469856","abstract_canon_sha256":"0f1136b4d28de1ba3e6c7c13630cb59db51d18e68d0c80a87cc1c15b3c10f6ac"},"schema_version":"1.0"},"canonical_sha256":"ab8a67cdc8c0d3f5e65001a991c0fa4644f5fbe0826413eeeb0a9e197d4d78e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:32.454978Z","signature_b64":"Bc3pV3or1+J8yJx+6tvmk+quOTRGpheUoQxMBTyWmIr0IGijEEYAUSLuPHO5S+RCz2WzMJnoQCnWOjveDTBLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab8a67cdc8c0d3f5e65001a991c0fa4644f5fbe0826413eeeb0a9e197d4d78e1","last_reissued_at":"2026-05-18T02:30:32.454601Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:32.454601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.4266","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":"2026-05-18T02:30:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z57mqpnFITFwoL9V2qbmvtqcWv7aIcD60+nQXvkERUy7DIKkfzpGsEI0QEZdXs38pKQ2GfvqBsrAjWOTqwkrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:59:30.680738Z"},"content_sha256":"148d217e999b52a707ea98962c27da92def7914fa64776e77cc761291b623668","schema_version":"1.0","event_id":"sha256:148d217e999b52a707ea98962c27da92def7914fa64776e77cc761291b623668"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:VOFGPTOIYDJ7LZSQAGUZDQH2IZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An invariance principle under the total variation distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guillaume Poly (FSTC), Ivan Nourdin (IECL)","submitted_at":"2013-10-16T04:29:01Z","abstract_excerpt":"Let $X_1,X_2,\\ldots$ be a sequence of i.i.d. random variables, with mean zero and variance one. Let $W_n=(X_1+\\ldots+X_n)/\\sqrt{n}$. An old and celebrated result of Prohorov asserts that $W_n$ converges in total variation to the standard Gaussian distribution if and only if $W_{n_0}$ has an absolutely continuous component for some $n_0$. In the present paper, we give yet another proof and extend Prohorov's theorem to a situation where, instead of $W_n$, we consider more generally a sequence of homogoneous polynomials in the $X_i$. More precisely, we exhibit conditions for a recent invariance p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4266","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":""},"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":"2026-05-18T02:30:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NqFYIeV6RNmmXgVzS7tuWHsJ9C5zcxhWnQX16Oi2cVqt7m0xJ8+xhXOSbhpm21mnFJy9LOsiUeYYIWVPK3OiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:59:30.681237Z"},"content_sha256":"e2dfd74af1159231bc6a0b6fb26f876e9ea10105a2df88587ac51572aa60dbec","schema_version":"1.0","event_id":"sha256:e2dfd74af1159231bc6a0b6fb26f876e9ea10105a2df88587ac51572aa60dbec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VOFGPTOIYDJ7LZSQAGUZDQH2IZ/bundle.json","state_url":"https://pith.science/pith/VOFGPTOIYDJ7LZSQAGUZDQH2IZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VOFGPTOIYDJ7LZSQAGUZDQH2IZ/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":"2026-05-26T11:59:30Z","links":{"resolver":"https://pith.science/pith/VOFGPTOIYDJ7LZSQAGUZDQH2IZ","bundle":"https://pith.science/pith/VOFGPTOIYDJ7LZSQAGUZDQH2IZ/bundle.json","state":"https://pith.science/pith/VOFGPTOIYDJ7LZSQAGUZDQH2IZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VOFGPTOIYDJ7LZSQAGUZDQH2IZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VOFGPTOIYDJ7LZSQAGUZDQH2IZ","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":"0f1136b4d28de1ba3e6c7c13630cb59db51d18e68d0c80a87cc1c15b3c10f6ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T04:29:01Z","title_canon_sha256":"01ce52c0dcb3d545a98bde6e2b29da3dda41c43e89f6ac19fb275a960f469856"},"schema_version":"1.0","source":{"id":"1310.4266","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4266","created_at":"2026-05-18T02:30:32Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4266v1","created_at":"2026-05-18T02:30:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4266","created_at":"2026-05-18T02:30:32Z"},{"alias_kind":"pith_short_12","alias_value":"VOFGPTOIYDJ7","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VOFGPTOIYDJ7LZSQ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VOFGPTOI","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:e2dfd74af1159231bc6a0b6fb26f876e9ea10105a2df88587ac51572aa60dbec","target":"graph","created_at":"2026-05-18T02:30:32Z","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":"Let $X_1,X_2,\\ldots$ be a sequence of i.i.d. random variables, with mean zero and variance one. Let $W_n=(X_1+\\ldots+X_n)/\\sqrt{n}$. An old and celebrated result of Prohorov asserts that $W_n$ converges in total variation to the standard Gaussian distribution if and only if $W_{n_0}$ has an absolutely continuous component for some $n_0$. In the present paper, we give yet another proof and extend Prohorov's theorem to a situation where, instead of $W_n$, we consider more generally a sequence of homogoneous polynomials in the $X_i$. More precisely, we exhibit conditions for a recent invariance p","authors_text":"Guillaume Poly (FSTC), Ivan Nourdin (IECL)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T04:29:01Z","title":"An invariance principle under the total variation distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4266","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":"sha256:148d217e999b52a707ea98962c27da92def7914fa64776e77cc761291b623668","target":"record","created_at":"2026-05-18T02:30:32Z","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":"0f1136b4d28de1ba3e6c7c13630cb59db51d18e68d0c80a87cc1c15b3c10f6ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T04:29:01Z","title_canon_sha256":"01ce52c0dcb3d545a98bde6e2b29da3dda41c43e89f6ac19fb275a960f469856"},"schema_version":"1.0","source":{"id":"1310.4266","kind":"arxiv","version":1}},"canonical_sha256":"ab8a67cdc8c0d3f5e65001a991c0fa4644f5fbe0826413eeeb0a9e197d4d78e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab8a67cdc8c0d3f5e65001a991c0fa4644f5fbe0826413eeeb0a9e197d4d78e1","first_computed_at":"2026-05-18T02:30:32.454601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:32.454601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bc3pV3or1+J8yJx+6tvmk+quOTRGpheUoQxMBTyWmIr0IGijEEYAUSLuPHO5S+RCz2WzMJnoQCnWOjveDTBLDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:32.454978Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4266","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:148d217e999b52a707ea98962c27da92def7914fa64776e77cc761291b623668","sha256:e2dfd74af1159231bc6a0b6fb26f876e9ea10105a2df88587ac51572aa60dbec"],"state_sha256":"182aef40d8c22ca1077a753517cbc672efda73e252af07720dd883cd2447d4aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9IDXMWHCV5d0heEBUZJw0kr4iP/jreEz67tTDgJwqBnf1GVCfV/ZkI6+jzRLo60AaaReeNJGxUtni617p47VAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:59:30.684435Z","bundle_sha256":"35ceb3f0172713a9f7eecba6844ce5d1ee2a505ca0e8b044f6f718d9b2b116a7"}}