{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ES4JDH25QS3GRSSNQPNSKBP3O5","short_pith_number":"pith:ES4JDH25","canonical_record":{"source":{"id":"1209.5575","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-25T11:04:45Z","cross_cats_sorted":[],"title_canon_sha256":"30a3afb8ed0be2b18ee186be7bc233917acbddc1506277d642594ee54fdbc081","abstract_canon_sha256":"12e16349ac1b3ac476c1a5731ddaaafdd29cea282ab2eba1db8fd829dbc1f1c7"},"schema_version":"1.0"},"canonical_sha256":"24b8919f5d84b668ca4d83db2505fb774c3735aaa196870d9864f54ff5fd7934","source":{"kind":"arxiv","id":"1209.5575","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5575","created_at":"2026-05-18T03:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5575v1","created_at":"2026-05-18T03:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5575","created_at":"2026-05-18T03:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"ES4JDH25QS3G","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"ES4JDH25QS3GRSSN","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"ES4JDH25","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ES4JDH25QS3GRSSNQPNSKBP3O5","target":"record","payload":{"canonical_record":{"source":{"id":"1209.5575","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-25T11:04:45Z","cross_cats_sorted":[],"title_canon_sha256":"30a3afb8ed0be2b18ee186be7bc233917acbddc1506277d642594ee54fdbc081","abstract_canon_sha256":"12e16349ac1b3ac476c1a5731ddaaafdd29cea282ab2eba1db8fd829dbc1f1c7"},"schema_version":"1.0"},"canonical_sha256":"24b8919f5d84b668ca4d83db2505fb774c3735aaa196870d9864f54ff5fd7934","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:48.120494Z","signature_b64":"l2Af8tym5mZgYr0SIKXCFRIv2RHuYPUn1oKHRGZFINYfU+D3iLkZqQ7TCUeQdw7lQ+GE/URXV3xEOhYwuuHOAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24b8919f5d84b668ca4d83db2505fb774c3735aaa196870d9864f54ff5fd7934","last_reissued_at":"2026-05-18T03:44:48.119737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:48.119737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.5575","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":"2026-05-18T03:44:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QOvKP0Fz2pie4fjmqyBBWrr/Y0EVgc3HjXXps9n426QWHR9Z/9i7fvvO+v5boIbud0YeabjdM7J3Ne1IdXavBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:55:19.821724Z"},"content_sha256":"ed6d0c148a47f12b0aec96983d8c5a49a24549614e71d519c581dcbc77a502ce","schema_version":"1.0","event_id":"sha256:ed6d0c148a47f12b0aec96983d8c5a49a24549614e71d519c581dcbc77a502ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ES4JDH25QS3GRSSNQPNSKBP3O5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Elementary Proof of Jin's Theorem with a Bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mauro Di Nasso","submitted_at":"2012-09-25T11:04:45Z","abstract_excerpt":"We present a short proof of Jin's theorem which is entirely elementary, in the sense that no use is made of nonstandard analysis, ergodic theory, measure theory, ultrafilters, or other advanced tools. The given proof provides the explicit bound 1/c where c=BD(A)*BD(B) to the number of shifts of A+B that are needed to cover a thick set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5575","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":"2026-05-18T03:44:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OGWUFcQiuj+AL+Pz9EgFikD9zCU+aGSlB61XHv5PpgAwFmaYVBr6TOFlOl6098AQYk/dF+MHDiYE0VVxYMzyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:55:19.822313Z"},"content_sha256":"7e8208654d6d01e0d3f00ded611e502671c85e4fbaab54db47f828cf998ccf24","schema_version":"1.0","event_id":"sha256:7e8208654d6d01e0d3f00ded611e502671c85e4fbaab54db47f828cf998ccf24"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ES4JDH25QS3GRSSNQPNSKBP3O5/bundle.json","state_url":"https://pith.science/pith/ES4JDH25QS3GRSSNQPNSKBP3O5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ES4JDH25QS3GRSSNQPNSKBP3O5/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":"2026-05-27T11:55:19Z","links":{"resolver":"https://pith.science/pith/ES4JDH25QS3GRSSNQPNSKBP3O5","bundle":"https://pith.science/pith/ES4JDH25QS3GRSSNQPNSKBP3O5/bundle.json","state":"https://pith.science/pith/ES4JDH25QS3GRSSNQPNSKBP3O5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ES4JDH25QS3GRSSNQPNSKBP3O5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ES4JDH25QS3GRSSNQPNSKBP3O5","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":"12e16349ac1b3ac476c1a5731ddaaafdd29cea282ab2eba1db8fd829dbc1f1c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-25T11:04:45Z","title_canon_sha256":"30a3afb8ed0be2b18ee186be7bc233917acbddc1506277d642594ee54fdbc081"},"schema_version":"1.0","source":{"id":"1209.5575","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5575","created_at":"2026-05-18T03:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5575v1","created_at":"2026-05-18T03:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5575","created_at":"2026-05-18T03:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"ES4JDH25QS3G","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"ES4JDH25QS3GRSSN","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"ES4JDH25","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:7e8208654d6d01e0d3f00ded611e502671c85e4fbaab54db47f828cf998ccf24","target":"graph","created_at":"2026-05-18T03:44:48Z","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 a short proof of Jin's theorem which is entirely elementary, in the sense that no use is made of nonstandard analysis, ergodic theory, measure theory, ultrafilters, or other advanced tools. The given proof provides the explicit bound 1/c where c=BD(A)*BD(B) to the number of shifts of A+B that are needed to cover a thick set.","authors_text":"Mauro Di Nasso","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-25T11:04:45Z","title":"An Elementary Proof of Jin's Theorem with a Bound"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5575","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:ed6d0c148a47f12b0aec96983d8c5a49a24549614e71d519c581dcbc77a502ce","target":"record","created_at":"2026-05-18T03:44:48Z","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":"12e16349ac1b3ac476c1a5731ddaaafdd29cea282ab2eba1db8fd829dbc1f1c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-25T11:04:45Z","title_canon_sha256":"30a3afb8ed0be2b18ee186be7bc233917acbddc1506277d642594ee54fdbc081"},"schema_version":"1.0","source":{"id":"1209.5575","kind":"arxiv","version":1}},"canonical_sha256":"24b8919f5d84b668ca4d83db2505fb774c3735aaa196870d9864f54ff5fd7934","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24b8919f5d84b668ca4d83db2505fb774c3735aaa196870d9864f54ff5fd7934","first_computed_at":"2026-05-18T03:44:48.119737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:48.119737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l2Af8tym5mZgYr0SIKXCFRIv2RHuYPUn1oKHRGZFINYfU+D3iLkZqQ7TCUeQdw7lQ+GE/URXV3xEOhYwuuHOAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:48.120494Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.5575","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed6d0c148a47f12b0aec96983d8c5a49a24549614e71d519c581dcbc77a502ce","sha256:7e8208654d6d01e0d3f00ded611e502671c85e4fbaab54db47f828cf998ccf24"],"state_sha256":"dec7de72f6f30d06ce7e341c9919d08fa3ec46284be143d3d1e9d3c548afb2ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uTPV1+Slkcn2nG0+N0W0jkZ47esz5HKfNwcFe/HN9bpDBzAe/jH2mIyNweG7N9ROLjn0y9TPUyiCcvhHbhpSDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:55:19.825377Z","bundle_sha256":"a152eb75aea27f24a48b55a8663453813bcf3b3c98ce9d73efd9b8224bf062db"}}