{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:V3PUAUTSJAGKLQCWJP4OANYMRA","short_pith_number":"pith:V3PUAUTS","schema_version":"1.0","canonical_sha256":"aedf405272480ca5c0564bf8e0370c88314c8b3e74623a256bae420178ad4385","source":{"kind":"arxiv","id":"2606.29260","version":1},"attestation_state":"computed","paper":{"title":"Digroups, their canonical pretorsion theory, and diheaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alberto Facchini, Carmelo Antonio Finocchiaro","submitted_at":"2026-06-28T08:14:44Z","abstract_excerpt":"In the category of digroups there is a natural pretorsion theory in which the torsion-free digroups are all groups, and torsion digroups form a category isomorphic to the category of non-empty sets. It is also possible to extend the theory of heaps from groups to digroups. The corresponding notion is that of a diheap."},"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":"2606.29260","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-28T08:14:44Z","cross_cats_sorted":[],"title_canon_sha256":"e72f06ba0c1b0bdc1fea5804e3829335e4ce3343b67c20aa948d682dd8c80ebe","abstract_canon_sha256":"c4366a77fb01a11bcdeb90bc2cfa227e03329777a390b9fe2cff8b3eb4dcaca9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:17:59.432951Z","signature_b64":"ZStJ2A3WDgcn/Xa2T4XL0jqyyeyyBmSVoP/cmrXJPJblSRKQs/fMZN0t6qxICXYaV/bALkZW8wwE0Q5yU8gXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aedf405272480ca5c0564bf8e0370c88314c8b3e74623a256bae420178ad4385","last_reissued_at":"2026-06-30T01:17:59.432478Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:17:59.432478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Digroups, their canonical pretorsion theory, and diheaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alberto Facchini, Carmelo Antonio Finocchiaro","submitted_at":"2026-06-28T08:14:44Z","abstract_excerpt":"In the category of digroups there is a natural pretorsion theory in which the torsion-free digroups are all groups, and torsion digroups form a category isomorphic to the category of non-empty sets. It is also possible to extend the theory of heaps from groups to digroups. The corresponding notion is that of a diheap."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29260","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.29260/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.29260","created_at":"2026-06-30T01:17:59.432543+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.29260v1","created_at":"2026-06-30T01:17:59.432543+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29260","created_at":"2026-06-30T01:17:59.432543+00:00"},{"alias_kind":"pith_short_12","alias_value":"V3PUAUTSJAGK","created_at":"2026-06-30T01:17:59.432543+00:00"},{"alias_kind":"pith_short_16","alias_value":"V3PUAUTSJAGKLQCW","created_at":"2026-06-30T01:17:59.432543+00:00"},{"alias_kind":"pith_short_8","alias_value":"V3PUAUTS","created_at":"2026-06-30T01:17:59.432543+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/V3PUAUTSJAGKLQCWJP4OANYMRA","json":"https://pith.science/pith/V3PUAUTSJAGKLQCWJP4OANYMRA.json","graph_json":"https://pith.science/api/pith-number/V3PUAUTSJAGKLQCWJP4OANYMRA/graph.json","events_json":"https://pith.science/api/pith-number/V3PUAUTSJAGKLQCWJP4OANYMRA/events.json","paper":"https://pith.science/paper/V3PUAUTS"},"agent_actions":{"view_html":"https://pith.science/pith/V3PUAUTSJAGKLQCWJP4OANYMRA","download_json":"https://pith.science/pith/V3PUAUTSJAGKLQCWJP4OANYMRA.json","view_paper":"https://pith.science/paper/V3PUAUTS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.29260&json=true","fetch_graph":"https://pith.science/api/pith-number/V3PUAUTSJAGKLQCWJP4OANYMRA/graph.json","fetch_events":"https://pith.science/api/pith-number/V3PUAUTSJAGKLQCWJP4OANYMRA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V3PUAUTSJAGKLQCWJP4OANYMRA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V3PUAUTSJAGKLQCWJP4OANYMRA/action/storage_attestation","attest_author":"https://pith.science/pith/V3PUAUTSJAGKLQCWJP4OANYMRA/action/author_attestation","sign_citation":"https://pith.science/pith/V3PUAUTSJAGKLQCWJP4OANYMRA/action/citation_signature","submit_replication":"https://pith.science/pith/V3PUAUTSJAGKLQCWJP4OANYMRA/action/replication_record"}},"created_at":"2026-06-30T01:17:59.432543+00:00","updated_at":"2026-06-30T01:17:59.432543+00:00"}