{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DMWSLO2Y23WHAR4RHB3MWI24IY","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":"33f9d401260376bd297c2edc3df2a8a30a9f0ddfc07bebe08e35a81ee8dfaf74","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AC","submitted_at":"2025-01-13T13:31:01Z","title_canon_sha256":"2d5767eb3e604bcd0c2f4d6508c02eda4f35b012ab6409241c8896cec3469d3a"},"schema_version":"1.0","source":{"id":"2501.07319","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.07319","created_at":"2026-07-05T10:50:32Z"},{"alias_kind":"arxiv_version","alias_value":"2501.07319v3","created_at":"2026-07-05T10:50:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.07319","created_at":"2026-07-05T10:50:32Z"},{"alias_kind":"pith_short_12","alias_value":"DMWSLO2Y23WH","created_at":"2026-07-05T10:50:32Z"},{"alias_kind":"pith_short_16","alias_value":"DMWSLO2Y23WHAR4R","created_at":"2026-07-05T10:50:32Z"},{"alias_kind":"pith_short_8","alias_value":"DMWSLO2Y","created_at":"2026-07-05T10:50:32Z"}],"graph_snapshots":[{"event_id":"sha256:954353d8de8836f5f9bd0d120def3f782bcf158ae639e7833d17efe7e11eb879","target":"graph","created_at":"2026-07-05T10:50:32Z","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/2501.07319/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be a finite simple graph, and let $I(G)$ denote its edge ideal. In this paper, we investigate the asymptotic behavior of the syzygies of powers of edge ideals through the lens of homological shift ideals $\\text{HS}_i(I(G)^k)$. We introduce the notion of the $i$th homological strong persistence property for monomial ideals $I$, providing an algebraic characterization that ensures the chain of inclusions $\\text{Ass}\\,\\text{HS}_i(I)\\subseteq\\text{Ass}\\,\\text{HS}_i(I^2)\\subseteq\\text{Ass}\\,\\text{HS}_i(I^3) \\subseteq\\cdots$. We prove that edge ideals possess both the $0$th and $1$st homolog","authors_text":"Antonino Ficarra, Ayesha Asloob Qureshi","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AC","submitted_at":"2025-01-13T13:31:01Z","title":"Edge ideals and their asymptotic syzygies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.07319","kind":"arxiv","version":3},"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:b88596827522dee5b88475e39ef6502645ebda5a888947df3310724ab5cb0609","target":"record","created_at":"2026-07-05T10:50:32Z","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":"33f9d401260376bd297c2edc3df2a8a30a9f0ddfc07bebe08e35a81ee8dfaf74","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AC","submitted_at":"2025-01-13T13:31:01Z","title_canon_sha256":"2d5767eb3e604bcd0c2f4d6508c02eda4f35b012ab6409241c8896cec3469d3a"},"schema_version":"1.0","source":{"id":"2501.07319","kind":"arxiv","version":3}},"canonical_sha256":"1b2d25bb58d6ec7047913876cb235c461e744a40c26e793da0042653bf27a707","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b2d25bb58d6ec7047913876cb235c461e744a40c26e793da0042653bf27a707","first_computed_at":"2026-07-05T10:50:32.043885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:50:32.043885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KQgQx/Ru8mYsXFNgz0sLPIFmVBeWxdzLbtFd2S4J+qIsk1fw4/zKKroopkrXHHMSI6G/2nbPGk4eVSQutYoDCw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:50:32.044420Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.07319","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b88596827522dee5b88475e39ef6502645ebda5a888947df3310724ab5cb0609","sha256:954353d8de8836f5f9bd0d120def3f782bcf158ae639e7833d17efe7e11eb879"],"state_sha256":"66fc237d08fcadf4a6f23df8374f0cfefa02ef0c43c1f989c3079099d52fa120"}