{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:H6ZVLPIEOU7SFHBFYYGWWVCF33","short_pith_number":"pith:H6ZVLPIE","canonical_record":{"source":{"id":"1807.11412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T16:05:12Z","cross_cats_sorted":[],"title_canon_sha256":"b95da71e4d362b41bfeb33e579c88710deda93ceeb8e4d542910cc21f99ca6d2","abstract_canon_sha256":"1ad43c03b9be30e7cb5801454947eed181b34f5a30f4eb5482a0ec838fd647b7"},"schema_version":"1.0"},"canonical_sha256":"3fb355bd04753f229c25c60d6b5445dec782e2c018e7d0f8d06b9cf10b5226ae","source":{"kind":"arxiv","id":"1807.11412","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11412","created_at":"2026-05-17T23:57:46Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11412v2","created_at":"2026-05-17T23:57:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11412","created_at":"2026-05-17T23:57:46Z"},{"alias_kind":"pith_short_12","alias_value":"H6ZVLPIEOU7S","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H6ZVLPIEOU7SFHBF","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H6ZVLPIE","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:H6ZVLPIEOU7SFHBFYYGWWVCF33","target":"record","payload":{"canonical_record":{"source":{"id":"1807.11412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T16:05:12Z","cross_cats_sorted":[],"title_canon_sha256":"b95da71e4d362b41bfeb33e579c88710deda93ceeb8e4d542910cc21f99ca6d2","abstract_canon_sha256":"1ad43c03b9be30e7cb5801454947eed181b34f5a30f4eb5482a0ec838fd647b7"},"schema_version":"1.0"},"canonical_sha256":"3fb355bd04753f229c25c60d6b5445dec782e2c018e7d0f8d06b9cf10b5226ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:46.686780Z","signature_b64":"li/qRY8yAk9jaGo7TiqKcP/dfez/LBQYkeB/H4nS7lZJEw/oamyXwH54LnpOrD8TRIUgNQkUxdNUSS0bnP/FBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fb355bd04753f229c25c60d6b5445dec782e2c018e7d0f8d06b9cf10b5226ae","last_reissued_at":"2026-05-17T23:57:46.686342Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:46.686342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.11412","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":"2026-05-17T23:57:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vUPstruATstKINK8qOy9WaT+PJSCMuFOxF+tZN8LREEuVWXa1oQ9T8OpH5Y+mQeeJWaWni01uuWiH2U+54KpBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:41:35.550705Z"},"content_sha256":"1258069b40a27fab40d4866742c0669251a2803ba8a69891d2e57f25b5755eb8","schema_version":"1.0","event_id":"sha256:1258069b40a27fab40d4866742c0669251a2803ba8a69891d2e57f25b5755eb8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:H6ZVLPIEOU7SFHBFYYGWWVCF33","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost p-ary Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"B\\\"u\\c{s}ra \\\"Ozden, O\\u{g}uz Yayla","submitted_at":"2018-07-30T16:05:12Z","abstract_excerpt":"In this paper we study almost $p$-ary sequences and their autocorrelation coefficients. We first study the number $\\ell$ of distinct out-of-phase autocorrelation coefficients for an almost $p$-ary sequence of period $n+s$ with $s$ consecutive zero-symbols. We prove an upper bound and a lower bound on $\\ell$. It is shown that $\\ell$ can not be less than $\\min\\{s,p,n\\}$. In particular, it is shown that a nearly perfect sequence with at least two consecutive zero symbols does not exist. Next we define a new difference set, partial direct product difference set (PDPDS), and we prove the connection"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11412","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":"2026-05-17T23:57:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qym5enFPSUDlaU8Zr0f8PmIz1aDLjMym3Sp/kGZSAsiApmRQIUBbiLWaxllELBnSRWpfDuOwRxRbtQ7DJOhYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:41:35.551049Z"},"content_sha256":"5f298f637c4b9f71f9089d4f653bd6a816d3541da2f90e02ee3b9118d5de5575","schema_version":"1.0","event_id":"sha256:5f298f637c4b9f71f9089d4f653bd6a816d3541da2f90e02ee3b9118d5de5575"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H6ZVLPIEOU7SFHBFYYGWWVCF33/bundle.json","state_url":"https://pith.science/pith/H6ZVLPIEOU7SFHBFYYGWWVCF33/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H6ZVLPIEOU7SFHBFYYGWWVCF33/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":"2026-06-12T10:41:35Z","links":{"resolver":"https://pith.science/pith/H6ZVLPIEOU7SFHBFYYGWWVCF33","bundle":"https://pith.science/pith/H6ZVLPIEOU7SFHBFYYGWWVCF33/bundle.json","state":"https://pith.science/pith/H6ZVLPIEOU7SFHBFYYGWWVCF33/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H6ZVLPIEOU7SFHBFYYGWWVCF33/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:H6ZVLPIEOU7SFHBFYYGWWVCF33","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":"1ad43c03b9be30e7cb5801454947eed181b34f5a30f4eb5482a0ec838fd647b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T16:05:12Z","title_canon_sha256":"b95da71e4d362b41bfeb33e579c88710deda93ceeb8e4d542910cc21f99ca6d2"},"schema_version":"1.0","source":{"id":"1807.11412","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11412","created_at":"2026-05-17T23:57:46Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11412v2","created_at":"2026-05-17T23:57:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11412","created_at":"2026-05-17T23:57:46Z"},{"alias_kind":"pith_short_12","alias_value":"H6ZVLPIEOU7S","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H6ZVLPIEOU7SFHBF","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H6ZVLPIE","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:5f298f637c4b9f71f9089d4f653bd6a816d3541da2f90e02ee3b9118d5de5575","target":"graph","created_at":"2026-05-17T23:57:46Z","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":"In this paper we study almost $p$-ary sequences and their autocorrelation coefficients. We first study the number $\\ell$ of distinct out-of-phase autocorrelation coefficients for an almost $p$-ary sequence of period $n+s$ with $s$ consecutive zero-symbols. We prove an upper bound and a lower bound on $\\ell$. It is shown that $\\ell$ can not be less than $\\min\\{s,p,n\\}$. In particular, it is shown that a nearly perfect sequence with at least two consecutive zero symbols does not exist. Next we define a new difference set, partial direct product difference set (PDPDS), and we prove the connection","authors_text":"B\\\"u\\c{s}ra \\\"Ozden, O\\u{g}uz Yayla","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T16:05:12Z","title":"Almost p-ary Sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11412","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":"sha256:1258069b40a27fab40d4866742c0669251a2803ba8a69891d2e57f25b5755eb8","target":"record","created_at":"2026-05-17T23:57:46Z","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":"1ad43c03b9be30e7cb5801454947eed181b34f5a30f4eb5482a0ec838fd647b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T16:05:12Z","title_canon_sha256":"b95da71e4d362b41bfeb33e579c88710deda93ceeb8e4d542910cc21f99ca6d2"},"schema_version":"1.0","source":{"id":"1807.11412","kind":"arxiv","version":2}},"canonical_sha256":"3fb355bd04753f229c25c60d6b5445dec782e2c018e7d0f8d06b9cf10b5226ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fb355bd04753f229c25c60d6b5445dec782e2c018e7d0f8d06b9cf10b5226ae","first_computed_at":"2026-05-17T23:57:46.686342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:46.686342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"li/qRY8yAk9jaGo7TiqKcP/dfez/LBQYkeB/H4nS7lZJEw/oamyXwH54LnpOrD8TRIUgNQkUxdNUSS0bnP/FBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:46.686780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.11412","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1258069b40a27fab40d4866742c0669251a2803ba8a69891d2e57f25b5755eb8","sha256:5f298f637c4b9f71f9089d4f653bd6a816d3541da2f90e02ee3b9118d5de5575"],"state_sha256":"4a40df460eb420820dbdac8aa81da30cddea7db44ac0ae760943ca6ca907da29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dClx9K7rKObfTlnQWd6YfKHHRdeCh2BgTKXbrZ+AAnUmATZO00eLzYL0FSVHAI85YCDrtCnrYP7UyNRn3E5oDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T10:41:35.553507Z","bundle_sha256":"28186a06f4766ed0f1fa287b00a728ebfa76c2136b2d7d7216ed70d46fed99ce"}}