{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:S236NAEB5FXVG2E45C3ASI3EQW","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":"600e0f45af8955b0979aa13104d1d3964ba52b740d543f7c6779d66c71a00a94","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.FA","submitted_at":"2007-05-03T06:17:03Z","title_canon_sha256":"b872cfa070775e19f2316e8f4c98571ed0a0f10808deef637bef1bd316074052"},"schema_version":"1.0","source":{"id":"0705.0411","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.0411","created_at":"2026-05-18T01:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"0705.0411v2","created_at":"2026-05-18T01:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.0411","created_at":"2026-05-18T01:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"S236NAEB5FXV","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"S236NAEB5FXVG2E4","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"S236NAEB","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:bfdc87a900573e9b5efe2b6f5f33e20484ffe3e7cb12aa9ac251d18ceec89f09","target":"graph","created_at":"2026-05-18T01:33:59Z","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":"Finite metric trees are known to have strict 1-negative type. In this paper we introduce a new family of inequalities that quantify the extent of the \"strictness\" of the 1-negative type inequalities for finite metric trees. These inequalities of \"enhanced 1-negative type\" are sufficiently strong to imply that any given finite metric tree must have strict p-negative type for all values of p in an open interval that contains the number 1. Moreover, these open intervals can be characterized purely in terms of the unordered distribution of edge weights that determine the path metric on the particu","authors_text":"Anthony Weston, Ian Doust","cross_cats":["math.MG"],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"2007-05-03T06:17:03Z","title":"Enhanced negative type for finite metric trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.0411","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":"sha256:7d1b7301a3c859784f7dce92b7b4a4466fcb891942af1a0de73b3e8139b028ac","target":"record","created_at":"2026-05-18T01:33:59Z","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":"600e0f45af8955b0979aa13104d1d3964ba52b740d543f7c6779d66c71a00a94","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.FA","submitted_at":"2007-05-03T06:17:03Z","title_canon_sha256":"b872cfa070775e19f2316e8f4c98571ed0a0f10808deef637bef1bd316074052"},"schema_version":"1.0","source":{"id":"0705.0411","kind":"arxiv","version":2}},"canonical_sha256":"96b7e68081e96f53689ce8b6092364858c1e577c35d05df4567ef8525e78837c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96b7e68081e96f53689ce8b6092364858c1e577c35d05df4567ef8525e78837c","first_computed_at":"2026-05-18T01:33:59.000763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:59.000763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CF23zGoFUetWD10625EEskm+eEw/tS9MhMUvxxk7QoLwgCw1zTc18Q9XdDkRGkdO/ohe9k2dAD49ggj5p1f7Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:59.001335Z","signed_message":"canonical_sha256_bytes"},"source_id":"0705.0411","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d1b7301a3c859784f7dce92b7b4a4466fcb891942af1a0de73b3e8139b028ac","sha256:bfdc87a900573e9b5efe2b6f5f33e20484ffe3e7cb12aa9ac251d18ceec89f09"],"state_sha256":"0eca4baf5c23965a8815cf8d2dd799625361e5be03b814b0964f12621f9663b0"}