{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VR4P4QISANCJS6W344DLNPRVV5","short_pith_number":"pith:VR4P4QIS","canonical_record":{"source":{"id":"1410.2725","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-10T10:14:26Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"0f7a603f7e04ba65ed69f5633feace78592ab367c634317c67a880e91ce2e503","abstract_canon_sha256":"87206ebf3fbe84dbf7b9ec0a1bd2a06c8b9c06e6e72d223cbcfd5b64e1746bd1"},"schema_version":"1.0"},"canonical_sha256":"ac78fe41120344997adbe706b6be35af5632c492c06feccb227f9ff7bafdf6c3","source":{"kind":"arxiv","id":"1410.2725","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2725","created_at":"2026-05-18T02:40:37Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2725v1","created_at":"2026-05-18T02:40:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2725","created_at":"2026-05-18T02:40:37Z"},{"alias_kind":"pith_short_12","alias_value":"VR4P4QISANCJ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VR4P4QISANCJS6W3","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VR4P4QIS","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VR4P4QISANCJS6W344DLNPRVV5","target":"record","payload":{"canonical_record":{"source":{"id":"1410.2725","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-10T10:14:26Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"0f7a603f7e04ba65ed69f5633feace78592ab367c634317c67a880e91ce2e503","abstract_canon_sha256":"87206ebf3fbe84dbf7b9ec0a1bd2a06c8b9c06e6e72d223cbcfd5b64e1746bd1"},"schema_version":"1.0"},"canonical_sha256":"ac78fe41120344997adbe706b6be35af5632c492c06feccb227f9ff7bafdf6c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:37.371699Z","signature_b64":"WmuTH7rV4MjLzfSmlYfFucz50V62+i2dVgZBUZ5aA6u02Sium3GtOrgmYJiKuZeVxMjas59BMpSGO8WSuNnBCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac78fe41120344997adbe706b6be35af5632c492c06feccb227f9ff7bafdf6c3","last_reissued_at":"2026-05-18T02:40:37.371097Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:37.371097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.2725","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":"2026-05-18T02:40:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7wV9bjCHx0p8vXxglFnzSV5k/JwjWZgwBJmx03C2S6Ej+ICQQycjINtcYuIDtoBzs0v8vhts10/b+XggMPSEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:49:34.162445Z"},"content_sha256":"cc17053a89d7311e0c5e0d4b76f44d066a79037cac4ffaa4f3fdc9d9c5134ba7","schema_version":"1.0","event_id":"sha256:cc17053a89d7311e0c5e0d4b76f44d066a79037cac4ffaa4f3fdc9d9c5134ba7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VR4P4QISANCJS6W344DLNPRVV5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Bounds of Certain Maximal Linear Codes in a Projective Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"B. Sundar Rajan, Srikanth Pai","submitted_at":"2014-10-10T10:14:26Z","abstract_excerpt":"The set of all subspaces of $\\mathbb{F}_q^n$ is denoted by $\\mathbb{P}_q(n)$. The subspace distance $d_S(X,Y) = \\dim(X)+ \\dim(Y) - 2\\dim(X \\cap Y)$ defined on $\\mathbb{P}_q(n)$ turns it into a natural coding space for error correction in random network coding. A subset of $\\mathbb{P}_q(n)$ is called a code and the subspaces that belong to the code are called codewords. Motivated by classical coding theory, a linear coding structure can be imposed on a subset of $\\mathbb{P}_q(n)$. Braun, Etzion and Vardy conjectured that the largest cardinality of a linear code, that contains $\\mathbb{F}_q^n$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2725","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":""},"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":"2026-05-18T02:40:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lQYlSh5Ey1ba1WNPPjs/bJmDD54x+JUon3Jr1QUs66PkBYyR2+tGrLzMGqIhK/YZUSKC3yFPuLgkh6GN01fPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:49:34.163187Z"},"content_sha256":"0489605cd3695ccd4c73aead144e0639b257a79c6c1c68eb2087c93604f587fb","schema_version":"1.0","event_id":"sha256:0489605cd3695ccd4c73aead144e0639b257a79c6c1c68eb2087c93604f587fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VR4P4QISANCJS6W344DLNPRVV5/bundle.json","state_url":"https://pith.science/pith/VR4P4QISANCJS6W344DLNPRVV5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VR4P4QISANCJS6W344DLNPRVV5/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":"2026-06-05T06:49:34Z","links":{"resolver":"https://pith.science/pith/VR4P4QISANCJS6W344DLNPRVV5","bundle":"https://pith.science/pith/VR4P4QISANCJS6W344DLNPRVV5/bundle.json","state":"https://pith.science/pith/VR4P4QISANCJS6W344DLNPRVV5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VR4P4QISANCJS6W344DLNPRVV5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VR4P4QISANCJS6W344DLNPRVV5","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":"87206ebf3fbe84dbf7b9ec0a1bd2a06c8b9c06e6e72d223cbcfd5b64e1746bd1","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-10T10:14:26Z","title_canon_sha256":"0f7a603f7e04ba65ed69f5633feace78592ab367c634317c67a880e91ce2e503"},"schema_version":"1.0","source":{"id":"1410.2725","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2725","created_at":"2026-05-18T02:40:37Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2725v1","created_at":"2026-05-18T02:40:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2725","created_at":"2026-05-18T02:40:37Z"},{"alias_kind":"pith_short_12","alias_value":"VR4P4QISANCJ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VR4P4QISANCJS6W3","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VR4P4QIS","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:0489605cd3695ccd4c73aead144e0639b257a79c6c1c68eb2087c93604f587fb","target":"graph","created_at":"2026-05-18T02:40:37Z","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":"The set of all subspaces of $\\mathbb{F}_q^n$ is denoted by $\\mathbb{P}_q(n)$. The subspace distance $d_S(X,Y) = \\dim(X)+ \\dim(Y) - 2\\dim(X \\cap Y)$ defined on $\\mathbb{P}_q(n)$ turns it into a natural coding space for error correction in random network coding. A subset of $\\mathbb{P}_q(n)$ is called a code and the subspaces that belong to the code are called codewords. Motivated by classical coding theory, a linear coding structure can be imposed on a subset of $\\mathbb{P}_q(n)$. Braun, Etzion and Vardy conjectured that the largest cardinality of a linear code, that contains $\\mathbb{F}_q^n$, ","authors_text":"B. Sundar Rajan, Srikanth Pai","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-10T10:14:26Z","title":"On the Bounds of Certain Maximal Linear Codes in a Projective Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2725","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:cc17053a89d7311e0c5e0d4b76f44d066a79037cac4ffaa4f3fdc9d9c5134ba7","target":"record","created_at":"2026-05-18T02:40:37Z","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":"87206ebf3fbe84dbf7b9ec0a1bd2a06c8b9c06e6e72d223cbcfd5b64e1746bd1","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-10T10:14:26Z","title_canon_sha256":"0f7a603f7e04ba65ed69f5633feace78592ab367c634317c67a880e91ce2e503"},"schema_version":"1.0","source":{"id":"1410.2725","kind":"arxiv","version":1}},"canonical_sha256":"ac78fe41120344997adbe706b6be35af5632c492c06feccb227f9ff7bafdf6c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac78fe41120344997adbe706b6be35af5632c492c06feccb227f9ff7bafdf6c3","first_computed_at":"2026-05-18T02:40:37.371097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:37.371097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WmuTH7rV4MjLzfSmlYfFucz50V62+i2dVgZBUZ5aA6u02Sium3GtOrgmYJiKuZeVxMjas59BMpSGO8WSuNnBCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:37.371699Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2725","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc17053a89d7311e0c5e0d4b76f44d066a79037cac4ffaa4f3fdc9d9c5134ba7","sha256:0489605cd3695ccd4c73aead144e0639b257a79c6c1c68eb2087c93604f587fb"],"state_sha256":"381cfc241e78458fe707defcc07d2914085039177cf5cb415bd039258d24b8e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hQ6DDQzS3l3wQCavFcQTxtQqOYjY2ENUVi3lT4o84wpn6FyZEOTeI+VQH+C0DdDpu4VSaaNi9CUPXUSaa8H0DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T06:49:34.166810Z","bundle_sha256":"756759f2ba85828afe47d121b5edd37ec4b14fc6b05cc252a24cdeb52bf523ba"}}