{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:P5AUVPWXUD3VLBAGEX5TOGIUEX","short_pith_number":"pith:P5AUVPWX","canonical_record":{"source":{"id":"2607.29020","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-31T04:47:27Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"9173774686b37e67cf6838d694b66694dfc7267f246f6ddf4fb8e89a2cdf432b","abstract_canon_sha256":"7f77660b0d51e00089fe19e3833d89bda209ed558d46be0ae30042d858fb575e"},"schema_version":"1.0"},"canonical_sha256":"7f414abed7a0f755840625fb37191425e7ad2c9c9f57137f091e8768f9435f73","source":{"kind":"arxiv","id":"2607.29020","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29020","created_at":"2026-08-03T01:18:07Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29020v1","created_at":"2026-08-03T01:18:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29020","created_at":"2026-08-03T01:18:07Z"},{"alias_kind":"pith_short_12","alias_value":"P5AUVPWXUD3V","created_at":"2026-08-03T01:18:07Z"},{"alias_kind":"pith_short_16","alias_value":"P5AUVPWXUD3VLBAG","created_at":"2026-08-03T01:18:07Z"},{"alias_kind":"pith_short_8","alias_value":"P5AUVPWX","created_at":"2026-08-03T01:18:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:P5AUVPWXUD3VLBAGEX5TOGIUEX","target":"record","payload":{"canonical_record":{"source":{"id":"2607.29020","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-31T04:47:27Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"9173774686b37e67cf6838d694b66694dfc7267f246f6ddf4fb8e89a2cdf432b","abstract_canon_sha256":"7f77660b0d51e00089fe19e3833d89bda209ed558d46be0ae30042d858fb575e"},"schema_version":"1.0"},"canonical_sha256":"7f414abed7a0f755840625fb37191425e7ad2c9c9f57137f091e8768f9435f73","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-03T01:18:07.370188Z","signature_b64":"U82Pe/tekD+gW5VrxWAvLxmnRXsH1jcyiV+3KtvhZhQBIz5u7giCedDRrP/bnDaCpa6r2CSWO+zppIjFlGFQCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f414abed7a0f755840625fb37191425e7ad2c9c9f57137f091e8768f9435f73","last_reissued_at":"2026-08-03T01:18:07.368667Z","signature_status":"signed_v1","first_computed_at":"2026-08-03T01:18:07.368667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.29020","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":"2026-08-03T01:18:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VCZ8A6Fygzfzhep4wPSmW0qNpwfXebz1pzoZ5FZvqYyky0i7OwezlVgXTbh69OtSnJRsdEiIsjGCcKhnjucnDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T23:20:20.384603Z"},"content_sha256":"6551ba08cb562b67c3dbcf1e00ed6c069e8cfbd86fa3ec0cc85d6ffbeb370cf9","schema_version":"1.0","event_id":"sha256:6551ba08cb562b67c3dbcf1e00ed6c069e8cfbd86fa3ec0cc85d6ffbeb370cf9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:P5AUVPWXUD3VLBAGEX5TOGIUEX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Entropic Symmetrization Resistance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.PR","authors_text":"Emma Pollard, Mokshay Madiman","submitted_at":"2026-07-31T04:47:27Z","abstract_excerpt":"An asymmetric random variable $X$ in the reals is said to be variance symmetrization resistant if every independent random variable $Y$ in the reals that produces a symmetric sum $X+Y$ has a greater variance than that of $X$. Asymmetric Bernoulli random variables were shown to be variance symmetrization resistant by Kagan, Mallows, Shepp, Vanderbei, and Vardi (1999); Pal (2008) gave a proof using stochastic calculus. We introduce the notion of entropic symmetrization resistance on locally compact groups-- this means that the entropy of any independent symmetrizer $Y$ must exceed that of $X$. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29020","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/2607.29020/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":"2026-08-03T01:18:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jF1Vz+P0yD2oBxoL93lIqMyXJVnZh+E9jPdzXGHli5zD2GRKAzOoyZhZnXbIfLqXdJ2p5iHMoYEbwGVsleSxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T23:20:20.385145Z"},"content_sha256":"b2fa524ede3482b07d8c782dc908df7e29abc0a8a0439a6a87e20a177343d633","schema_version":"1.0","event_id":"sha256:b2fa524ede3482b07d8c782dc908df7e29abc0a8a0439a6a87e20a177343d633"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P5AUVPWXUD3VLBAGEX5TOGIUEX/bundle.json","state_url":"https://pith.science/pith/P5AUVPWXUD3VLBAGEX5TOGIUEX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P5AUVPWXUD3VLBAGEX5TOGIUEX/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":"2026-08-03T23:20:20Z","links":{"resolver":"https://pith.science/pith/P5AUVPWXUD3VLBAGEX5TOGIUEX","bundle":"https://pith.science/pith/P5AUVPWXUD3VLBAGEX5TOGIUEX/bundle.json","state":"https://pith.science/pith/P5AUVPWXUD3VLBAGEX5TOGIUEX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P5AUVPWXUD3VLBAGEX5TOGIUEX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:P5AUVPWXUD3VLBAGEX5TOGIUEX","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":"7f77660b0d51e00089fe19e3833d89bda209ed558d46be0ae30042d858fb575e","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-31T04:47:27Z","title_canon_sha256":"9173774686b37e67cf6838d694b66694dfc7267f246f6ddf4fb8e89a2cdf432b"},"schema_version":"1.0","source":{"id":"2607.29020","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29020","created_at":"2026-08-03T01:18:07Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29020v1","created_at":"2026-08-03T01:18:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29020","created_at":"2026-08-03T01:18:07Z"},{"alias_kind":"pith_short_12","alias_value":"P5AUVPWXUD3V","created_at":"2026-08-03T01:18:07Z"},{"alias_kind":"pith_short_16","alias_value":"P5AUVPWXUD3VLBAG","created_at":"2026-08-03T01:18:07Z"},{"alias_kind":"pith_short_8","alias_value":"P5AUVPWX","created_at":"2026-08-03T01:18:07Z"}],"graph_snapshots":[{"event_id":"sha256:b2fa524ede3482b07d8c782dc908df7e29abc0a8a0439a6a87e20a177343d633","target":"graph","created_at":"2026-08-03T01:18:07Z","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/2607.29020/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An asymmetric random variable $X$ in the reals is said to be variance symmetrization resistant if every independent random variable $Y$ in the reals that produces a symmetric sum $X+Y$ has a greater variance than that of $X$. Asymmetric Bernoulli random variables were shown to be variance symmetrization resistant by Kagan, Mallows, Shepp, Vanderbei, and Vardi (1999); Pal (2008) gave a proof using stochastic calculus. We introduce the notion of entropic symmetrization resistance on locally compact groups-- this means that the entropy of any independent symmetrizer $Y$ must exceed that of $X$. W","authors_text":"Emma Pollard, Mokshay Madiman","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-31T04:47:27Z","title":"Entropic Symmetrization Resistance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29020","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":"sha256:6551ba08cb562b67c3dbcf1e00ed6c069e8cfbd86fa3ec0cc85d6ffbeb370cf9","target":"record","created_at":"2026-08-03T01:18:07Z","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":"7f77660b0d51e00089fe19e3833d89bda209ed558d46be0ae30042d858fb575e","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-31T04:47:27Z","title_canon_sha256":"9173774686b37e67cf6838d694b66694dfc7267f246f6ddf4fb8e89a2cdf432b"},"schema_version":"1.0","source":{"id":"2607.29020","kind":"arxiv","version":1}},"canonical_sha256":"7f414abed7a0f755840625fb37191425e7ad2c9c9f57137f091e8768f9435f73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f414abed7a0f755840625fb37191425e7ad2c9c9f57137f091e8768f9435f73","first_computed_at":"2026-08-03T01:18:07.368667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T01:18:07.368667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U82Pe/tekD+gW5VrxWAvLxmnRXsH1jcyiV+3KtvhZhQBIz5u7giCedDRrP/bnDaCpa6r2CSWO+zppIjFlGFQCg==","signature_status":"signed_v1","signed_at":"2026-08-03T01:18:07.370188Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.29020","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6551ba08cb562b67c3dbcf1e00ed6c069e8cfbd86fa3ec0cc85d6ffbeb370cf9","sha256:b2fa524ede3482b07d8c782dc908df7e29abc0a8a0439a6a87e20a177343d633"],"state_sha256":"afbe5fbfb92c956f8d2d96413de466bf4d501578f45e7f6360ba59b7bc0592c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QpV/ybstixcJ7Gpg6+SVRaVc+zuNPA1yIr/w3UvGajMlAxjDkRW0b0uiXSAQaUfVuUz/Q2wiIuKd9q9Rz3QtAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T23:20:20.388684Z","bundle_sha256":"66cd87407a2965ad881c77c2c0101867177f977956135a57e8731e107b56eaf1"}}