{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:R2DMOKAHRZDZAMTC3METYKHJ2K","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":"b70e48895ab1c7c1544e7e3c03a47322868971eaa1ed47d296c9b785ddcf178e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-13T17:05:41Z","title_canon_sha256":"8f9be0088f47cfe4dc3ded47d834458f7e6f0e08516997f60707e25b4f3bc36a"},"schema_version":"1.0","source":{"id":"1706.04164","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04164","created_at":"2026-05-18T00:42:24Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04164v1","created_at":"2026-05-18T00:42:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04164","created_at":"2026-05-18T00:42:24Z"},{"alias_kind":"pith_short_12","alias_value":"R2DMOKAHRZDZ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R2DMOKAHRZDZAMTC","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R2DMOKAH","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:c59f408826f47538f8edb51323ad875298922bfa73ff9ff0d43998ce8ad4a113","target":"graph","created_at":"2026-05-18T00:42:24Z","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":"Cools, Draisma, Payne, and Robeva proved that generic metric graphs that are \"paths of loops\" are Brill-Noether general. We show that Brill-Noether generality does not hold for \"trees of loops\": the only trees of loops that are Brill-Noether general are paths of loops. We study various notions of generality and examine which of these graphs satisfy them.","authors_text":"Nicholas Wawrykow, Sameer Kailasa, Vivian Kuperberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-13T17:05:41Z","title":"Chip-firing on trees of loops"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04164","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:dd5738e2f76792501f981e9956d192df2668316eed6ac654ded3b1b219429768","target":"record","created_at":"2026-05-18T00:42:24Z","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":"b70e48895ab1c7c1544e7e3c03a47322868971eaa1ed47d296c9b785ddcf178e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-13T17:05:41Z","title_canon_sha256":"8f9be0088f47cfe4dc3ded47d834458f7e6f0e08516997f60707e25b4f3bc36a"},"schema_version":"1.0","source":{"id":"1706.04164","kind":"arxiv","version":1}},"canonical_sha256":"8e86c728078e47903262db093c28e9d2a530f5bd5547bce6ac71c1b5a9358738","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e86c728078e47903262db093c28e9d2a530f5bd5547bce6ac71c1b5a9358738","first_computed_at":"2026-05-18T00:42:24.364900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:24.364900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M+WLCKigmx2DQMVuCrUsw+Y+FhyQzisyzvUwgKuYgCJqqAjsgzsejxq5DT413fyHhKceeHwIltkrtA3V0Qh7Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:24.365502Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04164","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd5738e2f76792501f981e9956d192df2668316eed6ac654ded3b1b219429768","sha256:c59f408826f47538f8edb51323ad875298922bfa73ff9ff0d43998ce8ad4a113"],"state_sha256":"2d159a3e2822ecbc6e83e339d71fe67b75e79b6aa02cb7425685bd3208c79bde"}