{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:B2Z52Y7MANA5UJ4MURIU5K3YAW","short_pith_number":"pith:B2Z52Y7M","canonical_record":{"source":{"id":"1002.3816","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2010-02-19T20:12:16Z","cross_cats_sorted":[],"title_canon_sha256":"9e9efa6febb23a78d3614f7a2493673e0921fe3af5bc6ebc413605302caab82a","abstract_canon_sha256":"129da8ef48232c20be3fa4874abcf59686c3d54dd1cc91f186b2478dd9168e22"},"schema_version":"1.0"},"canonical_sha256":"0eb3dd63ec0341da278ca4514eab780580232e9c00d636c6cf8116f29322a6ea","source":{"kind":"arxiv","id":"1002.3816","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3816","created_at":"2026-05-18T04:20:35Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3816v3","created_at":"2026-05-18T04:20:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3816","created_at":"2026-05-18T04:20:35Z"},{"alias_kind":"pith_short_12","alias_value":"B2Z52Y7MANA5","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"B2Z52Y7MANA5UJ4M","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"B2Z52Y7M","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:B2Z52Y7MANA5UJ4MURIU5K3YAW","target":"record","payload":{"canonical_record":{"source":{"id":"1002.3816","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2010-02-19T20:12:16Z","cross_cats_sorted":[],"title_canon_sha256":"9e9efa6febb23a78d3614f7a2493673e0921fe3af5bc6ebc413605302caab82a","abstract_canon_sha256":"129da8ef48232c20be3fa4874abcf59686c3d54dd1cc91f186b2478dd9168e22"},"schema_version":"1.0"},"canonical_sha256":"0eb3dd63ec0341da278ca4514eab780580232e9c00d636c6cf8116f29322a6ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:35.907839Z","signature_b64":"jGE/JJl7TObjgXWzjwxgf6r+xH/b1zVi5hQ75ylR+2Mj4e59MwkzmglrIHcqqq6x+R/yGzRknuMb+e1uprkLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0eb3dd63ec0341da278ca4514eab780580232e9c00d636c6cf8116f29322a6ea","last_reissued_at":"2026-05-18T04:20:35.906985Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:35.906985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.3816","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":"2026-05-18T04:20:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X+J1n9YUsEUESPOPfFyju0mVJUzK6aK0BzFHIhqYnUDqj2SoqSq1wySdjmVf6Osel60unRq1cp1FhYsxE/jGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T13:47:29.681325Z"},"content_sha256":"0a2aae5f3af5742131f17f08942658bc272f4e85b58032da0ce310bf719e43b5","schema_version":"1.0","event_id":"sha256:0a2aae5f3af5742131f17f08942658bc272f4e85b58032da0ce310bf719e43b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:B2Z52Y7MANA5UJ4MURIU5K3YAW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Note on Hypervector Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Sanjay Roy, T. K. Samanta","submitted_at":"2010-02-19T20:12:16Z","abstract_excerpt":"The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3816","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":"2026-05-18T04:20:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+4Sw5fD3//kzMHMJue0y7O6KLn8wmTfQC+pqcjn6KpmmTo5z44MpIUIglSGq3m+IBrxP4UOdz73+Ne8/gsuqCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T13:47:29.681667Z"},"content_sha256":"b3fab65e142c99fbe7549bd75afa4d5910c2dfb25748de1d3fc5686cf98cac8a","schema_version":"1.0","event_id":"sha256:b3fab65e142c99fbe7549bd75afa4d5910c2dfb25748de1d3fc5686cf98cac8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B2Z52Y7MANA5UJ4MURIU5K3YAW/bundle.json","state_url":"https://pith.science/pith/B2Z52Y7MANA5UJ4MURIU5K3YAW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B2Z52Y7MANA5UJ4MURIU5K3YAW/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":"2026-06-29T13:47:29Z","links":{"resolver":"https://pith.science/pith/B2Z52Y7MANA5UJ4MURIU5K3YAW","bundle":"https://pith.science/pith/B2Z52Y7MANA5UJ4MURIU5K3YAW/bundle.json","state":"https://pith.science/pith/B2Z52Y7MANA5UJ4MURIU5K3YAW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B2Z52Y7MANA5UJ4MURIU5K3YAW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:B2Z52Y7MANA5UJ4MURIU5K3YAW","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":"129da8ef48232c20be3fa4874abcf59686c3d54dd1cc91f186b2478dd9168e22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2010-02-19T20:12:16Z","title_canon_sha256":"9e9efa6febb23a78d3614f7a2493673e0921fe3af5bc6ebc413605302caab82a"},"schema_version":"1.0","source":{"id":"1002.3816","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3816","created_at":"2026-05-18T04:20:35Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3816v3","created_at":"2026-05-18T04:20:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3816","created_at":"2026-05-18T04:20:35Z"},{"alias_kind":"pith_short_12","alias_value":"B2Z52Y7MANA5","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"B2Z52Y7MANA5UJ4M","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"B2Z52Y7M","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:b3fab65e142c99fbe7549bd75afa4d5910c2dfb25748de1d3fc5686cf98cac8a","target":"graph","created_at":"2026-05-18T04:20:35Z","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 main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space.","authors_text":"Sanjay Roy, T. K. Samanta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2010-02-19T20:12:16Z","title":"A Note on Hypervector Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3816","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":"sha256:0a2aae5f3af5742131f17f08942658bc272f4e85b58032da0ce310bf719e43b5","target":"record","created_at":"2026-05-18T04:20:35Z","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":"129da8ef48232c20be3fa4874abcf59686c3d54dd1cc91f186b2478dd9168e22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2010-02-19T20:12:16Z","title_canon_sha256":"9e9efa6febb23a78d3614f7a2493673e0921fe3af5bc6ebc413605302caab82a"},"schema_version":"1.0","source":{"id":"1002.3816","kind":"arxiv","version":3}},"canonical_sha256":"0eb3dd63ec0341da278ca4514eab780580232e9c00d636c6cf8116f29322a6ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0eb3dd63ec0341da278ca4514eab780580232e9c00d636c6cf8116f29322a6ea","first_computed_at":"2026-05-18T04:20:35.906985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:35.906985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jGE/JJl7TObjgXWzjwxgf6r+xH/b1zVi5hQ75ylR+2Mj4e59MwkzmglrIHcqqq6x+R/yGzRknuMb+e1uprkLDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:35.907839Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.3816","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a2aae5f3af5742131f17f08942658bc272f4e85b58032da0ce310bf719e43b5","sha256:b3fab65e142c99fbe7549bd75afa4d5910c2dfb25748de1d3fc5686cf98cac8a"],"state_sha256":"a7e0ec42b073f42bb03e29d27de1de9109e330defc4cfecfb88ddbff06930b90"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jYLE74DLyQ/NfclILd5rxZUORWUoo2VAQTzsVrqGoiuLAQnPOaTHiuqgGYq0RFYhLTWwEyTEHy6VgiG9fUcDCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T13:47:29.683534Z","bundle_sha256":"cfed047f6b35d3952f3eaa719a0d726b6fa513359f72659772737b7232a75e78"}}