{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CBM7AGNSVAZQODKVEXPJGHTITC","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":"ff27733e89a0bcea4909a6d1411005176a5b55e1d86d13bae5cb0590998e936d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T21:21:46Z","title_canon_sha256":"78f8e825094198f9fbe124dfbbd6c0610eb0e308f8cd7f9e2b5c046bf39157d6"},"schema_version":"1.0","source":{"id":"2605.20504","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20504","created_at":"2026-05-21T01:04:40Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20504v1","created_at":"2026-05-21T01:04:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20504","created_at":"2026-05-21T01:04:40Z"},{"alias_kind":"pith_short_12","alias_value":"CBM7AGNSVAZQ","created_at":"2026-05-21T01:04:40Z"},{"alias_kind":"pith_short_16","alias_value":"CBM7AGNSVAZQODKV","created_at":"2026-05-21T01:04:40Z"},{"alias_kind":"pith_short_8","alias_value":"CBM7AGNS","created_at":"2026-05-21T01:04:40Z"}],"graph_snapshots":[{"event_id":"sha256:154aae855fa9b5c47d7e76f9d5296a2b9d44007b4b3b46fe6cba7811c4d95458","target":"graph","created_at":"2026-05-21T01:04:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.20504/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given balls and boxes both enumerated by the positive integers, we consider a sequential allocation of the balls into the boxes. We fix $\\ell \\ge 2$. Proceeding in increasing order of box labels, assign to each box the next $r$ smallest balls for some $ 1\\leq r\\leq\\ell$. Given an integer $k\\ge 3$, is there a natural number $N$ such that in any placement of $N$ balls into boxes, there exist $k$ balls whose labels and box labels each form a $k$-term arithmetic progression? We address this question by identifying abelian power-free fixed points of morphisms over a binary alphabet. We present suff","authors_text":"Haydar G\\\"oral, Nihan Tan{\\i}sal{\\i}, Sad{\\i}k Eyido\\u{g}an","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T21:21:46Z","title":"Box Progressions, Abelian Power-Free Morphisms and A Sieve Technique for the Template Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20504","kind":"arxiv","version":1},"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:ac11d6387db8834436e8043da6e8f4e6a7779de5f40d56c93d481f9889bf5856","target":"record","created_at":"2026-05-21T01:04:40Z","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":"ff27733e89a0bcea4909a6d1411005176a5b55e1d86d13bae5cb0590998e936d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T21:21:46Z","title_canon_sha256":"78f8e825094198f9fbe124dfbbd6c0610eb0e308f8cd7f9e2b5c046bf39157d6"},"schema_version":"1.0","source":{"id":"2605.20504","kind":"arxiv","version":1}},"canonical_sha256":"1059f019b2a833070d5525de931e68989078d9cc49b45f2482441618df89c5c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1059f019b2a833070d5525de931e68989078d9cc49b45f2482441618df89c5c9","first_computed_at":"2026-05-21T01:04:40.049190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:40.049190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FuR72v9LBE1b5MGqD+pw8DzuOvVixKq0DeoWb/dy0HgZmSA1sSAnYH6Aag4GKMjzDUR17mYM7kisj+TnkSKmBQ==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:40.049684Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20504","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac11d6387db8834436e8043da6e8f4e6a7779de5f40d56c93d481f9889bf5856","sha256:154aae855fa9b5c47d7e76f9d5296a2b9d44007b4b3b46fe6cba7811c4d95458"],"state_sha256":"ac90a4f20b27e3b26e6b5cf5ec9b0a867246489eef78c9f8162303890e2e559e"}