{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:LEWS7LGPJXNGH5F5TZESMCXHYV","short_pith_number":"pith:LEWS7LGP","schema_version":"1.0","canonical_sha256":"592d2faccf4dda63f4bd9e49260ae7c5470d4783d70106994148f05122004044","source":{"kind":"arxiv","id":"1005.5222","version":1},"attestation_state":"computed","paper":{"title":"Degenerations and orbits in finite abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.GR","authors_text":"Amritanshu Prasad, Kunal Dutta","submitted_at":"2010-05-28T06:22:35Z","abstract_excerpt":"A notion of degeneration of elements in groups is introduced. It is used to parametrize the orbits in a finite abelian group under its full automorphism group by a finite distributive lattice. A pictorial description of this lattice leads to an intuitive self-contained exposition of some of the basic facts concerning these orbits, including their enumeration. Given a partition $\\lambda$, the lattice parametrizing orbits in a finite abelian p-group of type $\\lambda$ is found to be independent of p. The order of the orbit corresponding to each parameter, which turns out to be a polynomial in p, "},"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":"1005.5222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-05-28T06:22:35Z","cross_cats_sorted":["math.CO","math.NT"],"title_canon_sha256":"4388750466f9a510c1df0aa2ce9e12fcdfede3cf7089a441c6693fdbc516828e","abstract_canon_sha256":"58e1803dac0c21a986295051fa467744cae9191a2b177eefd840191a46e960e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:45.343232Z","signature_b64":"rvC6LPu6ezKo4+IlGdvuNmMtrgPGVNR7UndDJhFTc4p9SkTInDnlDm8WxaLQLu6E6RNN4cTLbZZmCbHnyYd5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"592d2faccf4dda63f4bd9e49260ae7c5470d4783d70106994148f05122004044","last_reissued_at":"2026-05-18T04:27:45.342533Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:45.342533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Degenerations and orbits in finite abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.GR","authors_text":"Amritanshu Prasad, Kunal Dutta","submitted_at":"2010-05-28T06:22:35Z","abstract_excerpt":"A notion of degeneration of elements in groups is introduced. It is used to parametrize the orbits in a finite abelian group under its full automorphism group by a finite distributive lattice. A pictorial description of this lattice leads to an intuitive self-contained exposition of some of the basic facts concerning these orbits, including their enumeration. Given a partition $\\lambda$, the lattice parametrizing orbits in a finite abelian p-group of type $\\lambda$ is found to be independent of p. The order of the orbit corresponding to each parameter, which turns out to be a polynomial in p, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5222","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1005.5222","created_at":"2026-05-18T04:27:45.342651+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.5222v1","created_at":"2026-05-18T04:27:45.342651+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5222","created_at":"2026-05-18T04:27:45.342651+00:00"},{"alias_kind":"pith_short_12","alias_value":"LEWS7LGPJXNG","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"LEWS7LGPJXNGH5F5","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"LEWS7LGP","created_at":"2026-05-18T12:26:10.704358+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/LEWS7LGPJXNGH5F5TZESMCXHYV","json":"https://pith.science/pith/LEWS7LGPJXNGH5F5TZESMCXHYV.json","graph_json":"https://pith.science/api/pith-number/LEWS7LGPJXNGH5F5TZESMCXHYV/graph.json","events_json":"https://pith.science/api/pith-number/LEWS7LGPJXNGH5F5TZESMCXHYV/events.json","paper":"https://pith.science/paper/LEWS7LGP"},"agent_actions":{"view_html":"https://pith.science/pith/LEWS7LGPJXNGH5F5TZESMCXHYV","download_json":"https://pith.science/pith/LEWS7LGPJXNGH5F5TZESMCXHYV.json","view_paper":"https://pith.science/paper/LEWS7LGP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.5222&json=true","fetch_graph":"https://pith.science/api/pith-number/LEWS7LGPJXNGH5F5TZESMCXHYV/graph.json","fetch_events":"https://pith.science/api/pith-number/LEWS7LGPJXNGH5F5TZESMCXHYV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LEWS7LGPJXNGH5F5TZESMCXHYV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LEWS7LGPJXNGH5F5TZESMCXHYV/action/storage_attestation","attest_author":"https://pith.science/pith/LEWS7LGPJXNGH5F5TZESMCXHYV/action/author_attestation","sign_citation":"https://pith.science/pith/LEWS7LGPJXNGH5F5TZESMCXHYV/action/citation_signature","submit_replication":"https://pith.science/pith/LEWS7LGPJXNGH5F5TZESMCXHYV/action/replication_record"}},"created_at":"2026-05-18T04:27:45.342651+00:00","updated_at":"2026-05-18T04:27:45.342651+00:00"}