{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RRNMUXY6G6TXXYRIVW5KMUIJ47","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":"a0a70aff3808b7fde0716e5be112f00b27402e4045526c55d85b33b790975750","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-03T15:48:58Z","title_canon_sha256":"22f0f6fa05aa725628bbaaaf15c12ec5d45edd7f096d1d91fc6f2083644493d8"},"schema_version":"1.0","source":{"id":"1008.0583","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0583","created_at":"2026-05-18T04:42:42Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0583v1","created_at":"2026-05-18T04:42:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0583","created_at":"2026-05-18T04:42:42Z"},{"alias_kind":"pith_short_12","alias_value":"RRNMUXY6G6TX","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RRNMUXY6G6TXXYRI","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RRNMUXY6","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:5a5a711c4c4130b3125d86d475e7f65de8d60d2b165ace0125556ed118370129","target":"graph","created_at":"2026-05-18T04:42:42Z","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":"k is a field of characteristic p>0, and l_1,...,l_n are linear forms in k[x,y]. Intending applications to Hilbert--Kunz theory, to each triple C=(F,G,H) of nonzero homogeneous elements of k[x,y] we associate a function delta_C that encodes the \"syzygy gaps\" of F^q, G^q, and H^q*l_1^{a_1}*...*l_n^{a_n}, for all q=p^e and a_i<= q. These are close relatives of functions introduced in \"p-Fractals and power series--I\" [P. Monsky, P. Teixeira, p-Fractals and power series--I. Some 2 variable results, J. Algebra 280 (2004) 505--536]. Like their relatives, the delta_C exhibit surprising self-similarity","authors_text":"Pedro Teixeira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-03T15:48:58Z","title":"Syzygy gap fractals--I. Some structural results and an upper bound"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0583","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":"sha256:40a2a1ef5f36b22666c45bf8996fc04ebfc26e012b993592162a58dfd0676f1d","target":"record","created_at":"2026-05-18T04:42:42Z","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":"a0a70aff3808b7fde0716e5be112f00b27402e4045526c55d85b33b790975750","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-08-03T15:48:58Z","title_canon_sha256":"22f0f6fa05aa725628bbaaaf15c12ec5d45edd7f096d1d91fc6f2083644493d8"},"schema_version":"1.0","source":{"id":"1008.0583","kind":"arxiv","version":1}},"canonical_sha256":"8c5aca5f1e37a77be228adbaa65109e7df8ec46dbfd987c7a892988c9505c7a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c5aca5f1e37a77be228adbaa65109e7df8ec46dbfd987c7a892988c9505c7a7","first_computed_at":"2026-05-18T04:42:42.696175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:42.696175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cP6P1kZp4/bKNQEWJjwYYC+4t84+gzAMewBbyx4aXBagrL4/J6uMvyVqbXMhITj2mTNLkrpi4qfzO3OMcXyWCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:42.696749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.0583","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40a2a1ef5f36b22666c45bf8996fc04ebfc26e012b993592162a58dfd0676f1d","sha256:5a5a711c4c4130b3125d86d475e7f65de8d60d2b165ace0125556ed118370129"],"state_sha256":"c8ad24bdcd1fb3759e5108cfa7d59691e2b92e44aed295922e177eb3bc610b2e"}