{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:4N7HPTKZPMTYM4BVCVIBUPQX2C","short_pith_number":"pith:4N7HPTKZ","canonical_record":{"source":{"id":"2008.09944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-08-23T02:43:58Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"08ca7b3b216e71d9909c267dcf634dd57b8d2997d146dba5e4e64be6751d2863","abstract_canon_sha256":"8d6c8701072620a8450bc80aaa13867fa94f4e5b8543d3297b4ab4f999ba3d10"},"schema_version":"1.0"},"canonical_sha256":"e37e77cd597b2786703515501a3e17d0a36b484565af53da1064d219c0eb1719","source":{"kind":"arxiv","id":"2008.09944","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.09944","created_at":"2026-07-05T01:29:18Z"},{"alias_kind":"arxiv_version","alias_value":"2008.09944v1","created_at":"2026-07-05T01:29:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.09944","created_at":"2026-07-05T01:29:18Z"},{"alias_kind":"pith_short_12","alias_value":"4N7HPTKZPMTY","created_at":"2026-07-05T01:29:18Z"},{"alias_kind":"pith_short_16","alias_value":"4N7HPTKZPMTYM4BV","created_at":"2026-07-05T01:29:18Z"},{"alias_kind":"pith_short_8","alias_value":"4N7HPTKZ","created_at":"2026-07-05T01:29:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:4N7HPTKZPMTYM4BVCVIBUPQX2C","target":"record","payload":{"canonical_record":{"source":{"id":"2008.09944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-08-23T02:43:58Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"08ca7b3b216e71d9909c267dcf634dd57b8d2997d146dba5e4e64be6751d2863","abstract_canon_sha256":"8d6c8701072620a8450bc80aaa13867fa94f4e5b8543d3297b4ab4f999ba3d10"},"schema_version":"1.0"},"canonical_sha256":"e37e77cd597b2786703515501a3e17d0a36b484565af53da1064d219c0eb1719","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:29:18.981600Z","signature_b64":"MJH7UCeT16fk9yrXML8zzoN01+5Zy1BnZyh3pndNWIW/0DT4rP2318JAWT8vaBGnIEQFWUmDLB9q3+U2E2/CCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e37e77cd597b2786703515501a3e17d0a36b484565af53da1064d219c0eb1719","last_reissued_at":"2026-07-05T01:29:18.981153Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:29:18.981153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.09944","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":"2026-07-05T01:29:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4p6ye8a7g8pQ0Brxzz9gWDFlQhEk1QOzvewBop5C8sOjwsJKXxJ2QvpiNyCD7crfuFBmp+fYiESsiyOh7709BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T06:32:08.002657Z"},"content_sha256":"367904120741ec89ccddd8394ce86c0159e45a03a6441b28c19079e7b25bc72f","schema_version":"1.0","event_id":"sha256:367904120741ec89ccddd8394ce86c0159e45a03a6441b28c19079e7b25bc72f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:4N7HPTKZPMTYM4BVCVIBUPQX2C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parameter-controlled inserting constructions of constant dimension subspace codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hao Chen, Huimin Lao, Jian Weng, Xiaoqing Tan","submitted_at":"2020-08-23T02:43:58Z","abstract_excerpt":"A basic problem in constant dimension subspace coding is to determine the maximal possible size ${\\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces in ${\\bf F}_q^n$ such that the subspace distance satisfies $\\operatorname{dis}(U,V)=2k-2\\dim(U \\cap V) \\geq d$ for any two different $k$-dimensional subspaces $U$ and $V$ in this set. In this paper we propose new parameter-controlled inserting constructions of constant dimension subspace codes. These inserting constructions are flexible because they are controlled by parameters. Several new better lower bounds which are better than all previou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.09944","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.09944/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:29:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R4LulAz+4/DvbTdL000pZYsIqe59GcMuVS5XfTHW5B4k9pMDXL7v+HIr5o9ubZl0bSFQFFbMuM3UXak/BkwHBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T06:32:08.003044Z"},"content_sha256":"71f2f3291aab94e27d7d76e664b3e6702d9f07271e693cca7a05a8269c061d49","schema_version":"1.0","event_id":"sha256:71f2f3291aab94e27d7d76e664b3e6702d9f07271e693cca7a05a8269c061d49"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4N7HPTKZPMTYM4BVCVIBUPQX2C/bundle.json","state_url":"https://pith.science/pith/4N7HPTKZPMTYM4BVCVIBUPQX2C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4N7HPTKZPMTYM4BVCVIBUPQX2C/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":"2026-07-07T06:32:08Z","links":{"resolver":"https://pith.science/pith/4N7HPTKZPMTYM4BVCVIBUPQX2C","bundle":"https://pith.science/pith/4N7HPTKZPMTYM4BVCVIBUPQX2C/bundle.json","state":"https://pith.science/pith/4N7HPTKZPMTYM4BVCVIBUPQX2C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4N7HPTKZPMTYM4BVCVIBUPQX2C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:4N7HPTKZPMTYM4BVCVIBUPQX2C","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":"8d6c8701072620a8450bc80aaa13867fa94f4e5b8543d3297b4ab4f999ba3d10","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-08-23T02:43:58Z","title_canon_sha256":"08ca7b3b216e71d9909c267dcf634dd57b8d2997d146dba5e4e64be6751d2863"},"schema_version":"1.0","source":{"id":"2008.09944","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.09944","created_at":"2026-07-05T01:29:18Z"},{"alias_kind":"arxiv_version","alias_value":"2008.09944v1","created_at":"2026-07-05T01:29:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.09944","created_at":"2026-07-05T01:29:18Z"},{"alias_kind":"pith_short_12","alias_value":"4N7HPTKZPMTY","created_at":"2026-07-05T01:29:18Z"},{"alias_kind":"pith_short_16","alias_value":"4N7HPTKZPMTYM4BV","created_at":"2026-07-05T01:29:18Z"},{"alias_kind":"pith_short_8","alias_value":"4N7HPTKZ","created_at":"2026-07-05T01:29:18Z"}],"graph_snapshots":[{"event_id":"sha256:71f2f3291aab94e27d7d76e664b3e6702d9f07271e693cca7a05a8269c061d49","target":"graph","created_at":"2026-07-05T01:29:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.09944/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A basic problem in constant dimension subspace coding is to determine the maximal possible size ${\\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces in ${\\bf F}_q^n$ such that the subspace distance satisfies $\\operatorname{dis}(U,V)=2k-2\\dim(U \\cap V) \\geq d$ for any two different $k$-dimensional subspaces $U$ and $V$ in this set. In this paper we propose new parameter-controlled inserting constructions of constant dimension subspace codes. These inserting constructions are flexible because they are controlled by parameters. Several new better lower bounds which are better than all previou","authors_text":"Hao Chen, Huimin Lao, Jian Weng, Xiaoqing Tan","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-08-23T02:43:58Z","title":"Parameter-controlled inserting constructions of constant dimension subspace codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.09944","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":"sha256:367904120741ec89ccddd8394ce86c0159e45a03a6441b28c19079e7b25bc72f","target":"record","created_at":"2026-07-05T01:29:18Z","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":"8d6c8701072620a8450bc80aaa13867fa94f4e5b8543d3297b4ab4f999ba3d10","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-08-23T02:43:58Z","title_canon_sha256":"08ca7b3b216e71d9909c267dcf634dd57b8d2997d146dba5e4e64be6751d2863"},"schema_version":"1.0","source":{"id":"2008.09944","kind":"arxiv","version":1}},"canonical_sha256":"e37e77cd597b2786703515501a3e17d0a36b484565af53da1064d219c0eb1719","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e37e77cd597b2786703515501a3e17d0a36b484565af53da1064d219c0eb1719","first_computed_at":"2026-07-05T01:29:18.981153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:29:18.981153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MJH7UCeT16fk9yrXML8zzoN01+5Zy1BnZyh3pndNWIW/0DT4rP2318JAWT8vaBGnIEQFWUmDLB9q3+U2E2/CCw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:29:18.981600Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.09944","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:367904120741ec89ccddd8394ce86c0159e45a03a6441b28c19079e7b25bc72f","sha256:71f2f3291aab94e27d7d76e664b3e6702d9f07271e693cca7a05a8269c061d49"],"state_sha256":"eb860e04018c4087b5a4eb2bab761619e6219f08c6219dac2231dcc664a5799b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"47D7rKp1ve8aXpLuezU5Ncu6UT/JbbapGhCY5UDCVsKi0fxyn4jrCOis9Z16P+Qabf4neMF20+Pqn/HF+6/gCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T06:32:08.005197Z","bundle_sha256":"eb7bfcd3e6fa6406cb0282f64492a4e2904a31cb345eccb8d30356079b3919c4"}}