{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:OFOJJHFKHCDOGFMHXZJQ7TWRUQ","short_pith_number":"pith:OFOJJHFK","canonical_record":{"source":{"id":"0909.1599","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-09-09T01:01:52Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"549dc85b5581dd1cc1e4057694882f7d3058181afeaa53e42d2ebfc9d9102a67","abstract_canon_sha256":"d67395de3ba72fedbe5f6cbe314d139d5bd46fc03ad1222f04121b32620efdb9"},"schema_version":"1.0"},"canonical_sha256":"715c949caa3886e31587be530fced1a41685060dee9013116f4b11b895e035e4","source":{"kind":"arxiv","id":"0909.1599","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.1599","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"arxiv_version","alias_value":"0909.1599v3","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1599","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"pith_short_12","alias_value":"OFOJJHFKHCDO","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OFOJJHFKHCDOGFMH","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OFOJJHFK","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:OFOJJHFKHCDOGFMHXZJQ7TWRUQ","target":"record","payload":{"canonical_record":{"source":{"id":"0909.1599","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-09-09T01:01:52Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"549dc85b5581dd1cc1e4057694882f7d3058181afeaa53e42d2ebfc9d9102a67","abstract_canon_sha256":"d67395de3ba72fedbe5f6cbe314d139d5bd46fc03ad1222f04121b32620efdb9"},"schema_version":"1.0"},"canonical_sha256":"715c949caa3886e31587be530fced1a41685060dee9013116f4b11b895e035e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:48.241703Z","signature_b64":"5fTzaSrp3SUSacl2PSI5yFy5ANMNikaFCWu4A79IB2nEk3G79u6Nz/yUF5SATj7jJnHj52omSD3h8NvFbRdNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"715c949caa3886e31587be530fced1a41685060dee9013116f4b11b895e035e4","last_reissued_at":"2026-05-18T02:20:48.241004Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:48.241004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.1599","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:20:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m8kWpsXwMg7Ianwz1dSGYYKR2mnrJxibrm7b6e25oGvJUW9RrckYtJExKBp6lLgg/8bKIlR93Qr+/lCoRCjjCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:14:20.433410Z"},"content_sha256":"c2472cb52483d6b269291cf070f293cc251949743bd0c0862e4ff9308fad8b53","schema_version":"1.0","event_id":"sha256:c2472cb52483d6b269291cf070f293cc251949743bd0c0862e4ff9308fad8b53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:OFOJJHFKHCDOGFMHXZJQ7TWRUQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Frame Permutation Quantization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ha Q. Nguyen, Lav R. Varshney, Vivek K Goyal","submitted_at":"2009-09-09T01:01:52Z","abstract_excerpt":"Frame permutation quantization (FPQ) is a new vector quantization technique using finite frames. In FPQ, a vector is encoded using a permutation source code to quantize its frame expansion. This means that the encoding is a partial ordering of the frame expansion coefficients. Compared to ordinary permutation source coding, FPQ produces a greater number of possible quantization rates and a higher maximum rate. Various representations for the partitions induced by FPQ are presented, and reconstruction algorithms based on linear programming, quadratic programming, and recursive orthogonal projec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1599","kind":"arxiv","version":3},"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":"2026-05-18T02:20:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UEQWgFIBoT8y+lkJdqID/G+rqC0a1/AgK6JY5aC2GbN4JiP7vCOI/XqHa70a+toJxCgxkXoyyS7q+TuvQdqYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:14:20.434128Z"},"content_sha256":"772661da18510669b71035cec2d3f6064aa7a133012254a1d5a3fda4803f3cf9","schema_version":"1.0","event_id":"sha256:772661da18510669b71035cec2d3f6064aa7a133012254a1d5a3fda4803f3cf9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OFOJJHFKHCDOGFMHXZJQ7TWRUQ/bundle.json","state_url":"https://pith.science/pith/OFOJJHFKHCDOGFMHXZJQ7TWRUQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OFOJJHFKHCDOGFMHXZJQ7TWRUQ/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":"2026-05-28T21:14:20Z","links":{"resolver":"https://pith.science/pith/OFOJJHFKHCDOGFMHXZJQ7TWRUQ","bundle":"https://pith.science/pith/OFOJJHFKHCDOGFMHXZJQ7TWRUQ/bundle.json","state":"https://pith.science/pith/OFOJJHFKHCDOGFMHXZJQ7TWRUQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OFOJJHFKHCDOGFMHXZJQ7TWRUQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:OFOJJHFKHCDOGFMHXZJQ7TWRUQ","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":"d67395de3ba72fedbe5f6cbe314d139d5bd46fc03ad1222f04121b32620efdb9","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-09-09T01:01:52Z","title_canon_sha256":"549dc85b5581dd1cc1e4057694882f7d3058181afeaa53e42d2ebfc9d9102a67"},"schema_version":"1.0","source":{"id":"0909.1599","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.1599","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"arxiv_version","alias_value":"0909.1599v3","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1599","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"pith_short_12","alias_value":"OFOJJHFKHCDO","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OFOJJHFKHCDOGFMH","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OFOJJHFK","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:772661da18510669b71035cec2d3f6064aa7a133012254a1d5a3fda4803f3cf9","target":"graph","created_at":"2026-05-18T02:20:48Z","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":"Frame permutation quantization (FPQ) is a new vector quantization technique using finite frames. In FPQ, a vector is encoded using a permutation source code to quantize its frame expansion. This means that the encoding is a partial ordering of the frame expansion coefficients. Compared to ordinary permutation source coding, FPQ produces a greater number of possible quantization rates and a higher maximum rate. Various representations for the partitions induced by FPQ are presented, and reconstruction algorithms based on linear programming, quadratic programming, and recursive orthogonal projec","authors_text":"Ha Q. Nguyen, Lav R. Varshney, Vivek K Goyal","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-09-09T01:01:52Z","title":"Frame Permutation Quantization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1599","kind":"arxiv","version":3},"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:c2472cb52483d6b269291cf070f293cc251949743bd0c0862e4ff9308fad8b53","target":"record","created_at":"2026-05-18T02:20:48Z","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":"d67395de3ba72fedbe5f6cbe314d139d5bd46fc03ad1222f04121b32620efdb9","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-09-09T01:01:52Z","title_canon_sha256":"549dc85b5581dd1cc1e4057694882f7d3058181afeaa53e42d2ebfc9d9102a67"},"schema_version":"1.0","source":{"id":"0909.1599","kind":"arxiv","version":3}},"canonical_sha256":"715c949caa3886e31587be530fced1a41685060dee9013116f4b11b895e035e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"715c949caa3886e31587be530fced1a41685060dee9013116f4b11b895e035e4","first_computed_at":"2026-05-18T02:20:48.241004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:48.241004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5fTzaSrp3SUSacl2PSI5yFy5ANMNikaFCWu4A79IB2nEk3G79u6Nz/yUF5SATj7jJnHj52omSD3h8NvFbRdNDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:48.241703Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.1599","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2472cb52483d6b269291cf070f293cc251949743bd0c0862e4ff9308fad8b53","sha256:772661da18510669b71035cec2d3f6064aa7a133012254a1d5a3fda4803f3cf9"],"state_sha256":"7b8a7fe67cda15cdaed7cdebbe55ff59f8083e7bb3416facca2c984f736e1eea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"as/2Hf4vV2xG6CXH7D+gOj1NIcODbU7rP9bi2V5M0r1KxsNTOUg7w19aMNh/mqBegxHBGr0aMGqtbOgJAyqtBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:14:20.437764Z","bundle_sha256":"6eacf567358c8be8e86368ad8fed6e224584791b40f23220dbee00a9a96acf87"}}