{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6WI2EPUTELLB22E76KVIBABMPO","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":"57bcb37bf03051350556fa4734779d8c1c136a2195be14889ec681cf49b8bc22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-07T16:37:24Z","title_canon_sha256":"7b962afeb2bc8ac26e3b1519b7d78ba9a3b9337a0306e5a7ce40d75b4984e694"},"schema_version":"1.0","source":{"id":"1204.1654","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1654","created_at":"2026-05-17T23:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1654v2","created_at":"2026-05-17T23:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1654","created_at":"2026-05-17T23:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"6WI2EPUTELLB","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6WI2EPUTELLB22E7","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6WI2EPUT","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:d8f28b867db5fc8c93e10cae0eec4848a9b0b64444af6f577146cfc6b02096e9","target":"graph","created_at":"2026-05-17T23:42:14Z","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":"For an indecomposable module $M$ over a path algebra of a quiver of type $\\widetilde{\\mathbb A}_n$, the Gabriel-Roiter measure gives rise to four new numerical invariants; we call them the multiplicity, and the initial, periodic and final parts. We describe how these invariants for $M$ and for its dual specify the position of $M$ in the Auslander-Reiten quiver of the algebra.","authors_text":"Helene R. Tyler, Markus Schmidmeier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-07T16:37:24Z","title":"The Auslander-Reiten Components in the Rhombic Picture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1654","kind":"arxiv","version":2},"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":"sha256:7587732feb782303c8ec666a8b1d4b6982932b3ec9e399dd5acaa8b81bcaae55","target":"record","created_at":"2026-05-17T23:42:14Z","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":"57bcb37bf03051350556fa4734779d8c1c136a2195be14889ec681cf49b8bc22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-07T16:37:24Z","title_canon_sha256":"7b962afeb2bc8ac26e3b1519b7d78ba9a3b9337a0306e5a7ce40d75b4984e694"},"schema_version":"1.0","source":{"id":"1204.1654","kind":"arxiv","version":2}},"canonical_sha256":"f591a23e9322d61d689ff2aa80802c7ba30c2d06ad5397b27a2072c8f84ba864","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f591a23e9322d61d689ff2aa80802c7ba30c2d06ad5397b27a2072c8f84ba864","first_computed_at":"2026-05-17T23:42:14.626690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:14.626690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nPULID9GXmvOz8YhTbywoVVSD1tI4dcVf+fsUylB3+AOrcainlc5aNk4gac8lz5fzFfUU0v4XREoXOb7HIhCAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:14.627399Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1654","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7587732feb782303c8ec666a8b1d4b6982932b3ec9e399dd5acaa8b81bcaae55","sha256:d8f28b867db5fc8c93e10cae0eec4848a9b0b64444af6f577146cfc6b02096e9"],"state_sha256":"bb795bc94c9e6f4b57de69d0507c6e9db2b7c85c831466f5c90e2ed6fb7972a6"}