{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JW5UMKJDKSQC53L3Q3J3Q5PW7C","short_pith_number":"pith:JW5UMKJD","canonical_record":{"source":{"id":"1611.07144","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-11-22T04:35:14Z","cross_cats_sorted":["cs.CC","math.NT"],"title_canon_sha256":"28abd15c77fb1d5e73586bb763acda878129fdb515d3041a44ad5255d37acd57","abstract_canon_sha256":"62c7717ed88c5705b92d5cbab25957eab23aa3038338ab625cd7c361af9cb040"},"schema_version":"1.0"},"canonical_sha256":"4dbb46292354a02eed7b86d3b875f6f8bffd57025779b31298b782d88ece6ec1","source":{"kind":"arxiv","id":"1611.07144","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07144","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07144v2","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07144","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"pith_short_12","alias_value":"JW5UMKJDKSQC","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JW5UMKJDKSQC53L3","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JW5UMKJD","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JW5UMKJDKSQC53L3Q3J3Q5PW7C","target":"record","payload":{"canonical_record":{"source":{"id":"1611.07144","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-11-22T04:35:14Z","cross_cats_sorted":["cs.CC","math.NT"],"title_canon_sha256":"28abd15c77fb1d5e73586bb763acda878129fdb515d3041a44ad5255d37acd57","abstract_canon_sha256":"62c7717ed88c5705b92d5cbab25957eab23aa3038338ab625cd7c361af9cb040"},"schema_version":"1.0"},"canonical_sha256":"4dbb46292354a02eed7b86d3b875f6f8bffd57025779b31298b782d88ece6ec1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:51.116521Z","signature_b64":"Q0+DhnQNuNdNR3C29PiH4nbaTeGlODf0CQhfcnJjRjzNgzAVi+JTIUYEQrwD4rCvqOG+D5GfMpiAMlr9rU0sBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4dbb46292354a02eed7b86d3b875f6f8bffd57025779b31298b782d88ece6ec1","last_reissued_at":"2026-05-18T00:32:51.115896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:51.115896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.07144","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":"2026-05-18T00:32:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ibU0lFVCpC5oPVmpGjNkqF52J5P12YBcu39mHa2Enm3bs0pciu1tgolmvA6TTBuuAlxpHiCpmnaK7N5MWr4jBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:25:17.950475Z"},"content_sha256":"733a6c41bba0c27f4fc0ae6bbee8754c88c857fb69ef2f9566eca5396cdd3d16","schema_version":"1.0","event_id":"sha256:733a6c41bba0c27f4fc0ae6bbee8754c88c857fb69ef2f9566eca5396cdd3d16"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JW5UMKJDKSQC53L3Q3J3Q5PW7C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Faster integer multiplication using plain vanilla FFT primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.NT"],"primary_cat":"cs.SC","authors_text":"David Harvey, Joris van der Hoeven","submitted_at":"2016-11-22T04:35:14Z","abstract_excerpt":"Assuming a conjectural upper bound for the least prime in an arithmetic progression, we show that n-bit integers may be multiplied in O(n log n 4^(log^* n)) bit operations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07144","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":"2026-05-18T00:32:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wrJt5rUP8iOtV+6KRHpEpNwX6wtmYbEbWeL94Asbb5LByEoHgHeimxqZG88GckxsZWW0DT2kFcWCqbDmZ2ZRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:25:17.951183Z"},"content_sha256":"eef9322e182ad74894ee8fe166a87df4364316801a0afed86dc4978e7574a248","schema_version":"1.0","event_id":"sha256:eef9322e182ad74894ee8fe166a87df4364316801a0afed86dc4978e7574a248"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JW5UMKJDKSQC53L3Q3J3Q5PW7C/bundle.json","state_url":"https://pith.science/pith/JW5UMKJDKSQC53L3Q3J3Q5PW7C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JW5UMKJDKSQC53L3Q3J3Q5PW7C/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":"2026-06-08T18:25:17Z","links":{"resolver":"https://pith.science/pith/JW5UMKJDKSQC53L3Q3J3Q5PW7C","bundle":"https://pith.science/pith/JW5UMKJDKSQC53L3Q3J3Q5PW7C/bundle.json","state":"https://pith.science/pith/JW5UMKJDKSQC53L3Q3J3Q5PW7C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JW5UMKJDKSQC53L3Q3J3Q5PW7C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JW5UMKJDKSQC53L3Q3J3Q5PW7C","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":"62c7717ed88c5705b92d5cbab25957eab23aa3038338ab625cd7c361af9cb040","cross_cats_sorted":["cs.CC","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-11-22T04:35:14Z","title_canon_sha256":"28abd15c77fb1d5e73586bb763acda878129fdb515d3041a44ad5255d37acd57"},"schema_version":"1.0","source":{"id":"1611.07144","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07144","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07144v2","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07144","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"pith_short_12","alias_value":"JW5UMKJDKSQC","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JW5UMKJDKSQC53L3","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JW5UMKJD","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:eef9322e182ad74894ee8fe166a87df4364316801a0afed86dc4978e7574a248","target":"graph","created_at":"2026-05-18T00:32:51Z","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":"Assuming a conjectural upper bound for the least prime in an arithmetic progression, we show that n-bit integers may be multiplied in O(n log n 4^(log^* n)) bit operations.","authors_text":"David Harvey, Joris van der Hoeven","cross_cats":["cs.CC","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-11-22T04:35:14Z","title":"Faster integer multiplication using plain vanilla FFT primes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07144","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":"sha256:733a6c41bba0c27f4fc0ae6bbee8754c88c857fb69ef2f9566eca5396cdd3d16","target":"record","created_at":"2026-05-18T00:32:51Z","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":"62c7717ed88c5705b92d5cbab25957eab23aa3038338ab625cd7c361af9cb040","cross_cats_sorted":["cs.CC","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-11-22T04:35:14Z","title_canon_sha256":"28abd15c77fb1d5e73586bb763acda878129fdb515d3041a44ad5255d37acd57"},"schema_version":"1.0","source":{"id":"1611.07144","kind":"arxiv","version":2}},"canonical_sha256":"4dbb46292354a02eed7b86d3b875f6f8bffd57025779b31298b782d88ece6ec1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4dbb46292354a02eed7b86d3b875f6f8bffd57025779b31298b782d88ece6ec1","first_computed_at":"2026-05-18T00:32:51.115896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:51.115896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q0+DhnQNuNdNR3C29PiH4nbaTeGlODf0CQhfcnJjRjzNgzAVi+JTIUYEQrwD4rCvqOG+D5GfMpiAMlr9rU0sBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:51.116521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.07144","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:733a6c41bba0c27f4fc0ae6bbee8754c88c857fb69ef2f9566eca5396cdd3d16","sha256:eef9322e182ad74894ee8fe166a87df4364316801a0afed86dc4978e7574a248"],"state_sha256":"55c09edfaf0ca60a029fb337e292d624dba9b63c67724f79ac419c4ef8438e3c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xo3YhR2DRuKqdNP7scnhiXT4DflooEcqFTVH8va81CzE0+gcqBuRdj+00xY3sIGkziMFpB9ZlVi3hEgJBqSwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:25:17.954974Z","bundle_sha256":"0e849101208aa4605fdf7e3b9d420e37ec085c2fb80afa1c43f685ac7ded321d"}}