{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U6H4FVDHQT5GZ4I4ZAEFZ455F3","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":"c0e7942d8956e1c5b63a3840d9cf3f9cc746581089d7911d4f09510b473dc0d3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2018-07-17T15:19:19Z","title_canon_sha256":"e540f33ba9786058084d5868f3180c84746f82946e1f4918a95718c30e6909cb"},"schema_version":"1.0","source":{"id":"1807.06495","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06495","created_at":"2026-07-05T01:12:01Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06495v2","created_at":"2026-07-05T01:12:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06495","created_at":"2026-07-05T01:12:01Z"},{"alias_kind":"pith_short_12","alias_value":"U6H4FVDHQT5G","created_at":"2026-07-05T01:12:01Z"},{"alias_kind":"pith_short_16","alias_value":"U6H4FVDHQT5GZ4I4","created_at":"2026-07-05T01:12:01Z"},{"alias_kind":"pith_short_8","alias_value":"U6H4FVDH","created_at":"2026-07-05T01:12:01Z"}],"graph_snapshots":[{"event_id":"sha256:a3519b1eca778e7e6054cfbad3e2bd1809ad62038a9581509aac62a916e82d83","target":"graph","created_at":"2026-07-05T01:12:01Z","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/1807.06495/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Every set of natural numbers determines a generating function convergent for $q \\in (-1,1)$ whose behavior as $q \\rightarrow 1^-$ determines a germ. These germs admit a natural partial ordering that can be used to compare sets of natural numbers in a manner that generalizes both cardinality of finite sets and density of infinite sets. For any finite set $D$ of positive integers, call a set $S$ \"$D$-avoiding\" if no two elements of $S$ differ by an element of $D$. We study the problem of determining, for fixed $D$, all $D$-avoiding sets that are maximal in the germ order. In many cases, we can s","authors_text":"Aaron Abrams, Alexander Russell, Henry Landau, James Propp, Jamie Pommersheim, Zeph Landau","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2018-07-17T15:19:19Z","title":"Germ order for one-dimensional packings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06495","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:f1a6f261317ee79255b4872bf738ee5504cf53d038fe09c8b3a3bf7fc0a66e96","target":"record","created_at":"2026-07-05T01:12:01Z","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":"c0e7942d8956e1c5b63a3840d9cf3f9cc746581089d7911d4f09510b473dc0d3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2018-07-17T15:19:19Z","title_canon_sha256":"e540f33ba9786058084d5868f3180c84746f82946e1f4918a95718c30e6909cb"},"schema_version":"1.0","source":{"id":"1807.06495","kind":"arxiv","version":2}},"canonical_sha256":"a78fc2d46784fa6cf11cc8085cf3bd2ef921d0f5ce24a0bc7c379039b8b3b162","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a78fc2d46784fa6cf11cc8085cf3bd2ef921d0f5ce24a0bc7c379039b8b3b162","first_computed_at":"2026-07-05T01:12:01.305893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:12:01.305893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xynl/hvlOJwZjwbPMxZk/yPc3WfEGpnH1HQYOMZ2BiqtoMav7ZHZHSknNBYNQaEbdablq8UnOGRDkJxLy5W4DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:12:01.306339Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.06495","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1a6f261317ee79255b4872bf738ee5504cf53d038fe09c8b3a3bf7fc0a66e96","sha256:a3519b1eca778e7e6054cfbad3e2bd1809ad62038a9581509aac62a916e82d83"],"state_sha256":"27f03470b473fae60f7f594f86cb44520de550b0f7abc0cf9d44bb8aaeaa806f"}