{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:TD52CIIFGYOSXZY4RF6C5M77VM","short_pith_number":"pith:TD52CIIF","schema_version":"1.0","canonical_sha256":"98fba12105361d2be71c897c2eb3ffab035127bd769704aff4a94984f9b329a3","source":{"kind":"arxiv","id":"1412.5466","version":3},"attestation_state":"computed","paper":{"title":"Enumerative Coding for Line Polar Grassmannians with applications to codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Ilaria Cardinali, Luca Giuzzi","submitted_at":"2014-12-17T16:26:40Z","abstract_excerpt":"A $k$-polar Grassmannian is the geometry having as pointset the set of all $k$-dimensional subspaces of a vector space $V$ which are totally isotropic for a given non-degenerate bilinear form $\\mu$ defined on $V.$ Hence it can be regarded as a subgeometry of the ordinary $k$-Grassmannian. In this paper we deal with orthogonal line Grassmannians and with symplectic line Grassmannians, i.e. we assume $k=2$ and $\\mu$ a non-degenerate symmetric or alternating form. We will provide a method to efficiently enumerate the pointsets of both orthogonal and symplectic line Grassmannians. This has several"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1412.5466","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-12-17T16:26:40Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"d54d2f6d17188f868b554e416e054ad70bd0a9f5d3ae22b3c68d60d821b85de8","abstract_canon_sha256":"94239fa40860b21973b8e7f6ae09292a358671f0aed243800af6bd9a283e28c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:56.235923Z","signature_b64":"3JwG7JnhghyssOlYAexSo9UVX+fgauyiXAF84AXfJgvb2VJvZet9f2njs6KVVRBbLo9uzLDhnnzmNDX7kib7Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98fba12105361d2be71c897c2eb3ffab035127bd769704aff4a94984f9b329a3","last_reissued_at":"2026-05-18T00:18:56.235268Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:56.235268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Enumerative Coding for Line Polar Grassmannians with applications to codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Ilaria Cardinali, Luca Giuzzi","submitted_at":"2014-12-17T16:26:40Z","abstract_excerpt":"A $k$-polar Grassmannian is the geometry having as pointset the set of all $k$-dimensional subspaces of a vector space $V$ which are totally isotropic for a given non-degenerate bilinear form $\\mu$ defined on $V.$ Hence it can be regarded as a subgeometry of the ordinary $k$-Grassmannian. In this paper we deal with orthogonal line Grassmannians and with symplectic line Grassmannians, i.e. we assume $k=2$ and $\\mu$ a non-degenerate symmetric or alternating form. We will provide a method to efficiently enumerate the pointsets of both orthogonal and symplectic line Grassmannians. This has several"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5466","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1412.5466","created_at":"2026-05-18T00:18:56.235373+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.5466v3","created_at":"2026-05-18T00:18:56.235373+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5466","created_at":"2026-05-18T00:18:56.235373+00:00"},{"alias_kind":"pith_short_12","alias_value":"TD52CIIFGYOS","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"TD52CIIFGYOSXZY4","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"TD52CIIF","created_at":"2026-05-18T12:28:49.207871+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TD52CIIFGYOSXZY4RF6C5M77VM","json":"https://pith.science/pith/TD52CIIFGYOSXZY4RF6C5M77VM.json","graph_json":"https://pith.science/api/pith-number/TD52CIIFGYOSXZY4RF6C5M77VM/graph.json","events_json":"https://pith.science/api/pith-number/TD52CIIFGYOSXZY4RF6C5M77VM/events.json","paper":"https://pith.science/paper/TD52CIIF"},"agent_actions":{"view_html":"https://pith.science/pith/TD52CIIFGYOSXZY4RF6C5M77VM","download_json":"https://pith.science/pith/TD52CIIFGYOSXZY4RF6C5M77VM.json","view_paper":"https://pith.science/paper/TD52CIIF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.5466&json=true","fetch_graph":"https://pith.science/api/pith-number/TD52CIIFGYOSXZY4RF6C5M77VM/graph.json","fetch_events":"https://pith.science/api/pith-number/TD52CIIFGYOSXZY4RF6C5M77VM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TD52CIIFGYOSXZY4RF6C5M77VM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TD52CIIFGYOSXZY4RF6C5M77VM/action/storage_attestation","attest_author":"https://pith.science/pith/TD52CIIFGYOSXZY4RF6C5M77VM/action/author_attestation","sign_citation":"https://pith.science/pith/TD52CIIFGYOSXZY4RF6C5M77VM/action/citation_signature","submit_replication":"https://pith.science/pith/TD52CIIFGYOSXZY4RF6C5M77VM/action/replication_record"}},"created_at":"2026-05-18T00:18:56.235373+00:00","updated_at":"2026-05-18T00:18:56.235373+00:00"}