{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BLQCAOHANJEJOCEPGOF4WV7PO7","short_pith_number":"pith:BLQCAOHA","canonical_record":{"source":{"id":"1612.06016","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-19T00:52:17Z","cross_cats_sorted":[],"title_canon_sha256":"622cb1186b7279dfabe4c2ed6271b9a29725935ffcc439145b5e18ae32074732","abstract_canon_sha256":"3b7c3a283873699f6494c9b0847aa15fcb211cdcf617b47a2f6ca212ed2a2058"},"schema_version":"1.0"},"canonical_sha256":"0ae02038e06a4897088f338bcb57ef77d06b257f088b41ab879031ac4cb45b47","source":{"kind":"arxiv","id":"1612.06016","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06016","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06016v1","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06016","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"BLQCAOHANJEJ","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BLQCAOHANJEJOCEP","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BLQCAOHA","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BLQCAOHANJEJOCEPGOF4WV7PO7","target":"record","payload":{"canonical_record":{"source":{"id":"1612.06016","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-19T00:52:17Z","cross_cats_sorted":[],"title_canon_sha256":"622cb1186b7279dfabe4c2ed6271b9a29725935ffcc439145b5e18ae32074732","abstract_canon_sha256":"3b7c3a283873699f6494c9b0847aa15fcb211cdcf617b47a2f6ca212ed2a2058"},"schema_version":"1.0"},"canonical_sha256":"0ae02038e06a4897088f338bcb57ef77d06b257f088b41ab879031ac4cb45b47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:46.101817Z","signature_b64":"GTpYfpBPm0ngh9W2FUn/CqqXpzLbcYEf258y33+FyddmhDqzrSS+T/ee6HUlbuexDnVYjXi1G20XYLvJqqh7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ae02038e06a4897088f338bcb57ef77d06b257f088b41ab879031ac4cb45b47","last_reissued_at":"2026-05-18T00:54:46.101352Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:46.101352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.06016","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":"2026-05-18T00:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wi+BEG3ppXQFXRvdSxpBNL5zTCLX9EjGaVrFpN7oqhzpjEDTtQxkU0e6bdBiQ81/N2tgXzx5c4mGOxupbeNZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:43:56.345133Z"},"content_sha256":"7ff4b7ddaa1be1b2eaa91ec69921141f4026188c51384b63891a3e0ae196a1bd","schema_version":"1.0","event_id":"sha256:7ff4b7ddaa1be1b2eaa91ec69921141f4026188c51384b63891a3e0ae196a1bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BLQCAOHANJEJOCEPGOF4WV7PO7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Characterization of Constant-Sample Testable Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Eric Blais, Yuichi Yoshida","submitted_at":"2016-12-19T00:52:17Z","abstract_excerpt":"We characterize the set of properties of Boolean-valued functions on a finite domain $\\mathcal{X}$ that are testable with a constant number of samples. Specifically, we show that a property $\\mathcal{P}$ is testable with a constant number of samples if and only if it is (essentially) a $k$-part symmetric property for some constant $k$, where a property is {\\em $k$-part symmetric} if there is a partition $S_1,\\ldots,S_k$ of $\\mathcal{X}$ such that whether $f:\\mathcal{X} \\to \\{0,1\\}$ satisfies the property is determined solely by the densities of $f$ on $S_1,\\ldots,S_k$. We use this characteriza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06016","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":"2026-05-18T00:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q50DPs+yztTNxj8HFAPGV8ttsvckeR78/rPqEw4y0WsBY75EnxtC/hiV79lCui/cyxLkpMBp3syuLizuz61IAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:43:56.345488Z"},"content_sha256":"bc59a4bf2c626db28c6d719c9ae6544a8aa2bba3de00cb8203b79b80de605de2","schema_version":"1.0","event_id":"sha256:bc59a4bf2c626db28c6d719c9ae6544a8aa2bba3de00cb8203b79b80de605de2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BLQCAOHANJEJOCEPGOF4WV7PO7/bundle.json","state_url":"https://pith.science/pith/BLQCAOHANJEJOCEPGOF4WV7PO7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BLQCAOHANJEJOCEPGOF4WV7PO7/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":"2026-06-04T12:43:56Z","links":{"resolver":"https://pith.science/pith/BLQCAOHANJEJOCEPGOF4WV7PO7","bundle":"https://pith.science/pith/BLQCAOHANJEJOCEPGOF4WV7PO7/bundle.json","state":"https://pith.science/pith/BLQCAOHANJEJOCEPGOF4WV7PO7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BLQCAOHANJEJOCEPGOF4WV7PO7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BLQCAOHANJEJOCEPGOF4WV7PO7","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":"3b7c3a283873699f6494c9b0847aa15fcb211cdcf617b47a2f6ca212ed2a2058","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-19T00:52:17Z","title_canon_sha256":"622cb1186b7279dfabe4c2ed6271b9a29725935ffcc439145b5e18ae32074732"},"schema_version":"1.0","source":{"id":"1612.06016","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06016","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06016v1","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06016","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"BLQCAOHANJEJ","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BLQCAOHANJEJOCEP","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BLQCAOHA","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:bc59a4bf2c626db28c6d719c9ae6544a8aa2bba3de00cb8203b79b80de605de2","target":"graph","created_at":"2026-05-18T00:54:46Z","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 characterize the set of properties of Boolean-valued functions on a finite domain $\\mathcal{X}$ that are testable with a constant number of samples. Specifically, we show that a property $\\mathcal{P}$ is testable with a constant number of samples if and only if it is (essentially) a $k$-part symmetric property for some constant $k$, where a property is {\\em $k$-part symmetric} if there is a partition $S_1,\\ldots,S_k$ of $\\mathcal{X}$ such that whether $f:\\mathcal{X} \\to \\{0,1\\}$ satisfies the property is determined solely by the densities of $f$ on $S_1,\\ldots,S_k$. We use this characteriza","authors_text":"Eric Blais, Yuichi Yoshida","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-19T00:52:17Z","title":"A Characterization of Constant-Sample Testable Properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06016","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":"sha256:7ff4b7ddaa1be1b2eaa91ec69921141f4026188c51384b63891a3e0ae196a1bd","target":"record","created_at":"2026-05-18T00:54:46Z","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":"3b7c3a283873699f6494c9b0847aa15fcb211cdcf617b47a2f6ca212ed2a2058","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-19T00:52:17Z","title_canon_sha256":"622cb1186b7279dfabe4c2ed6271b9a29725935ffcc439145b5e18ae32074732"},"schema_version":"1.0","source":{"id":"1612.06016","kind":"arxiv","version":1}},"canonical_sha256":"0ae02038e06a4897088f338bcb57ef77d06b257f088b41ab879031ac4cb45b47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ae02038e06a4897088f338bcb57ef77d06b257f088b41ab879031ac4cb45b47","first_computed_at":"2026-05-18T00:54:46.101352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:46.101352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GTpYfpBPm0ngh9W2FUn/CqqXpzLbcYEf258y33+FyddmhDqzrSS+T/ee6HUlbuexDnVYjXi1G20XYLvJqqh7Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:46.101817Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06016","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ff4b7ddaa1be1b2eaa91ec69921141f4026188c51384b63891a3e0ae196a1bd","sha256:bc59a4bf2c626db28c6d719c9ae6544a8aa2bba3de00cb8203b79b80de605de2"],"state_sha256":"011b8dc91497b2a970b59ee4381060ace65fb544562505d813917d182f179f44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rPDkMBycea4/pAG14HxHPmALZwI/ovZmuufUdQIsIbznNt/YRK9ljFZsymeLFjW3ms3CqioUeeUaB6JUr15cDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T12:43:56.347460Z","bundle_sha256":"c25dde51ea74c915666e237ed052c5956d4a958e11ae89b9f817de544b173486"}}