{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:PXWWKC4U5CW2YNCP7BWEIWU6LX","short_pith_number":"pith:PXWWKC4U","canonical_record":{"source":{"id":"1007.1839","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-07-12T08:03:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9d7e5479ae335b34b015a487dbc0c36f204f47f9f6fa0ecb90310738d6723ece","abstract_canon_sha256":"a413290bb5b3fa71b4fe433e3cf1628509035df8649ae0e2fe55dc10cb535710"},"schema_version":"1.0"},"canonical_sha256":"7ded650b94e8adac344ff86c445a9e5deca8fe6d4775e855796a6d2b67cbc022","source":{"kind":"arxiv","id":"1007.1839","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.1839","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1007.1839v2","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1839","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"PXWWKC4U5CW2","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PXWWKC4U5CW2YNCP","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PXWWKC4U","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:PXWWKC4U5CW2YNCP7BWEIWU6LX","target":"record","payload":{"canonical_record":{"source":{"id":"1007.1839","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-07-12T08:03:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9d7e5479ae335b34b015a487dbc0c36f204f47f9f6fa0ecb90310738d6723ece","abstract_canon_sha256":"a413290bb5b3fa71b4fe433e3cf1628509035df8649ae0e2fe55dc10cb535710"},"schema_version":"1.0"},"canonical_sha256":"7ded650b94e8adac344ff86c445a9e5deca8fe6d4775e855796a6d2b67cbc022","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:27.846517Z","signature_b64":"5axqGHKmUlopLqVTZdIRLQFiznI9ZuSvqhbEdRxQichIOMQtKiDzQN5QDZXRBII8lnCnKECmJ1pBhm7LC34dBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ded650b94e8adac344ff86c445a9e5deca8fe6d4775e855796a6d2b67cbc022","last_reissued_at":"2026-05-18T04:05:27.845993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:27.845993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.1839","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":"2026-05-18T04:05:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cze/0Rfwl/2HUscdN7BASFPeNUMRnN66GROIHK8AUS0GwpsBGc3vu/Fm7XowDodVymz+5F55pOoTZEupMWBLBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:19:58.569374Z"},"content_sha256":"e717fd5a94c52dcdf5ec033cd63919efd0778d627d0f9d4c4a25de3f5047ccf8","schema_version":"1.0","event_id":"sha256:e717fd5a94c52dcdf5ec033cd63919efd0778d627d0f9d4c4a25de3f5047ccf8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:PXWWKC4U5CW2YNCP7BWEIWU6LX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The shifted primes and the multidimensional Szemeredi and polynomial van der Waerden theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DS","authors_text":"Alexander Leibman, Tamar Ziegler, Vitaly Bergelson","submitted_at":"2010-07-12T08:03:55Z","abstract_excerpt":"In this short note we establish new refinements of multidimensional Szemeredi and polynomial van der Waerden theorems along the shifted primes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1839","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":"2026-05-18T04:05:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zO9r2JjUX0MUxgrsJWhDDizXZAYBDqs9+fVBFOTjsy7fwzrFOw9HS9GHO3fh9UAWxkgOgknx1lRTHF7zur0bBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:19:58.570030Z"},"content_sha256":"93f6c2422114c141831aa8b904a58a05a8b9fea6dcf2d3d2b49ede66a5a474de","schema_version":"1.0","event_id":"sha256:93f6c2422114c141831aa8b904a58a05a8b9fea6dcf2d3d2b49ede66a5a474de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PXWWKC4U5CW2YNCP7BWEIWU6LX/bundle.json","state_url":"https://pith.science/pith/PXWWKC4U5CW2YNCP7BWEIWU6LX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PXWWKC4U5CW2YNCP7BWEIWU6LX/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":"2026-05-25T21:19:58Z","links":{"resolver":"https://pith.science/pith/PXWWKC4U5CW2YNCP7BWEIWU6LX","bundle":"https://pith.science/pith/PXWWKC4U5CW2YNCP7BWEIWU6LX/bundle.json","state":"https://pith.science/pith/PXWWKC4U5CW2YNCP7BWEIWU6LX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PXWWKC4U5CW2YNCP7BWEIWU6LX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PXWWKC4U5CW2YNCP7BWEIWU6LX","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":"a413290bb5b3fa71b4fe433e3cf1628509035df8649ae0e2fe55dc10cb535710","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-07-12T08:03:55Z","title_canon_sha256":"9d7e5479ae335b34b015a487dbc0c36f204f47f9f6fa0ecb90310738d6723ece"},"schema_version":"1.0","source":{"id":"1007.1839","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.1839","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1007.1839v2","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1839","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"PXWWKC4U5CW2","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PXWWKC4U5CW2YNCP","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PXWWKC4U","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:93f6c2422114c141831aa8b904a58a05a8b9fea6dcf2d3d2b49ede66a5a474de","target":"graph","created_at":"2026-05-18T04:05:27Z","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":"In this short note we establish new refinements of multidimensional Szemeredi and polynomial van der Waerden theorems along the shifted primes.","authors_text":"Alexander Leibman, Tamar Ziegler, Vitaly Bergelson","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-07-12T08:03:55Z","title":"The shifted primes and the multidimensional Szemeredi and polynomial van der Waerden theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1839","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:e717fd5a94c52dcdf5ec033cd63919efd0778d627d0f9d4c4a25de3f5047ccf8","target":"record","created_at":"2026-05-18T04:05:27Z","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":"a413290bb5b3fa71b4fe433e3cf1628509035df8649ae0e2fe55dc10cb535710","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-07-12T08:03:55Z","title_canon_sha256":"9d7e5479ae335b34b015a487dbc0c36f204f47f9f6fa0ecb90310738d6723ece"},"schema_version":"1.0","source":{"id":"1007.1839","kind":"arxiv","version":2}},"canonical_sha256":"7ded650b94e8adac344ff86c445a9e5deca8fe6d4775e855796a6d2b67cbc022","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ded650b94e8adac344ff86c445a9e5deca8fe6d4775e855796a6d2b67cbc022","first_computed_at":"2026-05-18T04:05:27.845993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:27.845993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5axqGHKmUlopLqVTZdIRLQFiznI9ZuSvqhbEdRxQichIOMQtKiDzQN5QDZXRBII8lnCnKECmJ1pBhm7LC34dBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:27.846517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.1839","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e717fd5a94c52dcdf5ec033cd63919efd0778d627d0f9d4c4a25de3f5047ccf8","sha256:93f6c2422114c141831aa8b904a58a05a8b9fea6dcf2d3d2b49ede66a5a474de"],"state_sha256":"02132908f23386772ac93f9e63d6da35926a38d41c0a30498d41a5bc6b2462bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tJMlYyACiWSNsfn3xM8a+EMJvzuNLKnEDzh4hfd9lNuRE6aDhT9/lz6dsg6QX37833o1FU/l6HxmYTfvdO6UBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:19:58.573416Z","bundle_sha256":"fffbdffc750369409b2b106d8a4530aa99ffeb8a569245c17aef2383adff186b"}}