{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NGWPED7HHBN4SJD2PWJ772OCXK","short_pith_number":"pith:NGWPED7H","canonical_record":{"source":{"id":"1605.06977","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-23T11:20:18Z","cross_cats_sorted":[],"title_canon_sha256":"30bd7d2a138535c86b5729428970778608c29aa037844d0c4438c50e80360361","abstract_canon_sha256":"740d4f66744a4da9272bc597c27d2d5557a338cf6618299a7dd267170ad9b6a5"},"schema_version":"1.0"},"canonical_sha256":"69acf20fe7385bc9247a7d93ffe9c2ba8962cc3697e746b7d1857c054115f8c7","source":{"kind":"arxiv","id":"1605.06977","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06977","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06977v2","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06977","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"pith_short_12","alias_value":"NGWPED7HHBN4","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NGWPED7HHBN4SJD2","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NGWPED7H","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NGWPED7HHBN4SJD2PWJ772OCXK","target":"record","payload":{"canonical_record":{"source":{"id":"1605.06977","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-23T11:20:18Z","cross_cats_sorted":[],"title_canon_sha256":"30bd7d2a138535c86b5729428970778608c29aa037844d0c4438c50e80360361","abstract_canon_sha256":"740d4f66744a4da9272bc597c27d2d5557a338cf6618299a7dd267170ad9b6a5"},"schema_version":"1.0"},"canonical_sha256":"69acf20fe7385bc9247a7d93ffe9c2ba8962cc3697e746b7d1857c054115f8c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:27.066437Z","signature_b64":"MvbcJBmujF78Z8IVHI7XxH0CrWso6D6wnPeTr0gLYlXlDdJJYJEW7GKWyyY2aTQnqin7t3xbpHpsFWGufJJmCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69acf20fe7385bc9247a7d93ffe9c2ba8962cc3697e746b7d1857c054115f8c7","last_reissued_at":"2026-05-17T23:54:27.065755Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:27.065755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.06977","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":"2026-05-17T23:54:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h72Eo6XVDV9qWOLqrBYsf8PIAunQLtlx4T2ZNnZhr3HHFcdvlzodIrkOilxqQ3mlwYAzM2xwdm6S4SqBiLEtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:24:30.844651Z"},"content_sha256":"e3bde9fdc13da07de5aaa43a7562bc85d1f04963d33d2297e505e0e361c1049d","schema_version":"1.0","event_id":"sha256:e3bde9fdc13da07de5aaa43a7562bc85d1f04963d33d2297e505e0e361c1049d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NGWPED7HHBN4SJD2PWJ772OCXK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some Types of Linear Combinations of Weyl-Heisenberg Wave Packet Frames Over Local Fields of Positive Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Lalit K. Vashisht","submitted_at":"2016-05-23T11:20:18Z","abstract_excerpt":"In this paper, we present necessary and sufficient conditions for some types of linear combination of frame elements (wave packet) to be a frame for $L^2(\\mathbb{K})$, where $\\mathbb{K}$ is a local field of positive characteristic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06977","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":"2026-05-17T23:54:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Yqu739D2nROn598soxAcqNyf9R7FIE9lIYi8S2aAm4ifEw+6JcbfBK+7DCLTihkGmRBUTaZDcVI5NCKa5sqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:24:30.845004Z"},"content_sha256":"8a6b956a911cdaa939fb3b037f8d17c01e082c5f04966642eb08f979a8c64e71","schema_version":"1.0","event_id":"sha256:8a6b956a911cdaa939fb3b037f8d17c01e082c5f04966642eb08f979a8c64e71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NGWPED7HHBN4SJD2PWJ772OCXK/bundle.json","state_url":"https://pith.science/pith/NGWPED7HHBN4SJD2PWJ772OCXK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NGWPED7HHBN4SJD2PWJ772OCXK/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":"2026-06-02T11:24:30Z","links":{"resolver":"https://pith.science/pith/NGWPED7HHBN4SJD2PWJ772OCXK","bundle":"https://pith.science/pith/NGWPED7HHBN4SJD2PWJ772OCXK/bundle.json","state":"https://pith.science/pith/NGWPED7HHBN4SJD2PWJ772OCXK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NGWPED7HHBN4SJD2PWJ772OCXK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NGWPED7HHBN4SJD2PWJ772OCXK","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":"740d4f66744a4da9272bc597c27d2d5557a338cf6618299a7dd267170ad9b6a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-23T11:20:18Z","title_canon_sha256":"30bd7d2a138535c86b5729428970778608c29aa037844d0c4438c50e80360361"},"schema_version":"1.0","source":{"id":"1605.06977","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06977","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06977v2","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06977","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"pith_short_12","alias_value":"NGWPED7HHBN4","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NGWPED7HHBN4SJD2","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NGWPED7H","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:8a6b956a911cdaa939fb3b037f8d17c01e082c5f04966642eb08f979a8c64e71","target":"graph","created_at":"2026-05-17T23:54:27Z","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 paper, we present necessary and sufficient conditions for some types of linear combination of frame elements (wave packet) to be a frame for $L^2(\\mathbb{K})$, where $\\mathbb{K}$ is a local field of positive characteristic.","authors_text":"Lalit K. Vashisht","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-23T11:20:18Z","title":"Some Types of Linear Combinations of Weyl-Heisenberg Wave Packet Frames Over Local Fields of Positive Characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06977","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:e3bde9fdc13da07de5aaa43a7562bc85d1f04963d33d2297e505e0e361c1049d","target":"record","created_at":"2026-05-17T23:54:27Z","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":"740d4f66744a4da9272bc597c27d2d5557a338cf6618299a7dd267170ad9b6a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-23T11:20:18Z","title_canon_sha256":"30bd7d2a138535c86b5729428970778608c29aa037844d0c4438c50e80360361"},"schema_version":"1.0","source":{"id":"1605.06977","kind":"arxiv","version":2}},"canonical_sha256":"69acf20fe7385bc9247a7d93ffe9c2ba8962cc3697e746b7d1857c054115f8c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69acf20fe7385bc9247a7d93ffe9c2ba8962cc3697e746b7d1857c054115f8c7","first_computed_at":"2026-05-17T23:54:27.065755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:27.065755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MvbcJBmujF78Z8IVHI7XxH0CrWso6D6wnPeTr0gLYlXlDdJJYJEW7GKWyyY2aTQnqin7t3xbpHpsFWGufJJmCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:27.066437Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.06977","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3bde9fdc13da07de5aaa43a7562bc85d1f04963d33d2297e505e0e361c1049d","sha256:8a6b956a911cdaa939fb3b037f8d17c01e082c5f04966642eb08f979a8c64e71"],"state_sha256":"801e54b43e7a93b31d8b306ff502fcc7e0d070ef92c0165529f877e9670fef6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wd7OTMhbaNCpSJS05qUh/bPVXnhJj8+95b928TOoD29idLUhzF7Tl7CsSfLvlBJdhkjcnbbybqytNJID5pTUDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T11:24:30.846909Z","bundle_sha256":"ba0f9fd0f9c4fa52a4892152f05726a90a36eb5d369b1e788a83f227d0bdf6dc"}}