{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PP53TG3MTI26HNPKTGSSI3CPAF","short_pith_number":"pith:PP53TG3M","schema_version":"1.0","canonical_sha256":"7bfbb99b6c9a35e3b5ea99a5246c4f0150c5e57eba806a026cc25299a7d8c49c","source":{"kind":"arxiv","id":"1603.09645","version":1},"attestation_state":"computed","paper":{"title":"$3$-pyramidal Steiner Triple Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gloria Rinaldi, Marco Buratti, Tommaso Traetta","submitted_at":"2016-03-31T15:39:35Z","abstract_excerpt":"A design is said to be $f$-pyramidal when it has an automorphism group which fixes $f$ points and acts sharply transitively on all the others. The problem of establishing the set of values of $v$ for which there exists an $f$-pyramidal Steiner triple system of order $v$ has been deeply investigated in the case $f=1$ but it remains open for a special class of values of $v$. The same problem for the next possible $f$, which is $f=3$, is here completely solved: there exists a $3$-pyramidal Steiner triple system of order $v$ if and only if $v\\equiv7,9,15$ (mod $24$) or $v\\equiv 3, 19$ (mod 48)."},"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":"1603.09645","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-31T15:39:35Z","cross_cats_sorted":[],"title_canon_sha256":"9fe27be45e9b0d93b72f9ffe50067c107489609b34825e9c8ae0def9292fa2b6","abstract_canon_sha256":"df3337fe700e85f7decba5d103807c0c606b77cede35fbf8dbe3a5372e8b87ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:58.002616Z","signature_b64":"wf7f8EbMYnEt1YMb7LWpOfSEB2nHk3icv/VAtIt1QrcxnzlGg6KyqIrqlEA8BtcmlhXlg+PyQf1gYN3GQxw9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bfbb99b6c9a35e3b5ea99a5246c4f0150c5e57eba806a026cc25299a7d8c49c","last_reissued_at":"2026-05-18T01:17:58.001820Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:58.001820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$3$-pyramidal Steiner Triple Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gloria Rinaldi, Marco Buratti, Tommaso Traetta","submitted_at":"2016-03-31T15:39:35Z","abstract_excerpt":"A design is said to be $f$-pyramidal when it has an automorphism group which fixes $f$ points and acts sharply transitively on all the others. The problem of establishing the set of values of $v$ for which there exists an $f$-pyramidal Steiner triple system of order $v$ has been deeply investigated in the case $f=1$ but it remains open for a special class of values of $v$. The same problem for the next possible $f$, which is $f=3$, is here completely solved: there exists a $3$-pyramidal Steiner triple system of order $v$ if and only if $v\\equiv7,9,15$ (mod $24$) or $v\\equiv 3, 19$ (mod 48)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09645","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":"1603.09645","created_at":"2026-05-18T01:17:58.001956+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.09645v1","created_at":"2026-05-18T01:17:58.001956+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.09645","created_at":"2026-05-18T01:17:58.001956+00:00"},{"alias_kind":"pith_short_12","alias_value":"PP53TG3MTI26","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PP53TG3MTI26HNPK","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PP53TG3M","created_at":"2026-05-18T12:30:39.010887+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/PP53TG3MTI26HNPKTGSSI3CPAF","json":"https://pith.science/pith/PP53TG3MTI26HNPKTGSSI3CPAF.json","graph_json":"https://pith.science/api/pith-number/PP53TG3MTI26HNPKTGSSI3CPAF/graph.json","events_json":"https://pith.science/api/pith-number/PP53TG3MTI26HNPKTGSSI3CPAF/events.json","paper":"https://pith.science/paper/PP53TG3M"},"agent_actions":{"view_html":"https://pith.science/pith/PP53TG3MTI26HNPKTGSSI3CPAF","download_json":"https://pith.science/pith/PP53TG3MTI26HNPKTGSSI3CPAF.json","view_paper":"https://pith.science/paper/PP53TG3M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.09645&json=true","fetch_graph":"https://pith.science/api/pith-number/PP53TG3MTI26HNPKTGSSI3CPAF/graph.json","fetch_events":"https://pith.science/api/pith-number/PP53TG3MTI26HNPKTGSSI3CPAF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PP53TG3MTI26HNPKTGSSI3CPAF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PP53TG3MTI26HNPKTGSSI3CPAF/action/storage_attestation","attest_author":"https://pith.science/pith/PP53TG3MTI26HNPKTGSSI3CPAF/action/author_attestation","sign_citation":"https://pith.science/pith/PP53TG3MTI26HNPKTGSSI3CPAF/action/citation_signature","submit_replication":"https://pith.science/pith/PP53TG3MTI26HNPKTGSSI3CPAF/action/replication_record"}},"created_at":"2026-05-18T01:17:58.001956+00:00","updated_at":"2026-05-18T01:17:58.001956+00:00"}