{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IQSFE4LO543TAER2TPOCLKHV6Q","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":"044dd07842a03de5eb0b1884423fa6db81b48cb3b02c561c6892a43a82f02ac1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-09T16:06:18Z","title_canon_sha256":"8ac78fe339474283f5c97d07899c4e5f489f11cf618fdc793c1e8a9435e5364f"},"schema_version":"1.0","source":{"id":"2507.06977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.06977","created_at":"2026-07-05T11:34:26Z"},{"alias_kind":"arxiv_version","alias_value":"2507.06977v1","created_at":"2026-07-05T11:34:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.06977","created_at":"2026-07-05T11:34:26Z"},{"alias_kind":"pith_short_12","alias_value":"IQSFE4LO543T","created_at":"2026-07-05T11:34:26Z"},{"alias_kind":"pith_short_16","alias_value":"IQSFE4LO543TAER2","created_at":"2026-07-05T11:34:26Z"},{"alias_kind":"pith_short_8","alias_value":"IQSFE4LO","created_at":"2026-07-05T11:34:26Z"}],"graph_snapshots":[{"event_id":"sha256:59cad5d1de0372b80161dfedc91c2ac71eb77e98005de2ef0ad11994d0bac61f","target":"graph","created_at":"2026-07-05T11:34:26Z","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/2507.06977/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce novel variations on several well-known model-theoretic tree properties, and prove several equivalences to known properties. Motivated by the study of generalized indiscernibles, we introduce the notion of the $\\calI$-tree property ($\\calI$-TP), for an arbitrary Ramsey index structure $\\calI$. We focus attention on the colored linear order index structure \\textbf{c}, showing that \\textbf{c}-TP is equivalent to instability. After introducing \\textbf{c}-$\\TPi$ and \\textbf{c}-$\\TPii$, we prove that \\textbf{c}-$\\TPi$ is equivalent to $\\TPi$, and that \\textbf{c}-$\\TPii$ i","authors_text":"Gabriel Day","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-09T16:06:18Z","title":"Results on Colored Tree Properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06977","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":"sha256:89a349730c223acef67c8941df7fd4f389f91c366a205814918631183489e03c","target":"record","created_at":"2026-07-05T11:34:26Z","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":"044dd07842a03de5eb0b1884423fa6db81b48cb3b02c561c6892a43a82f02ac1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-09T16:06:18Z","title_canon_sha256":"8ac78fe339474283f5c97d07899c4e5f489f11cf618fdc793c1e8a9435e5364f"},"schema_version":"1.0","source":{"id":"2507.06977","kind":"arxiv","version":1}},"canonical_sha256":"442452716eef3730123a9bdc25a8f5f43e935399dc81845d848c50a2ed25869a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"442452716eef3730123a9bdc25a8f5f43e935399dc81845d848c50a2ed25869a","first_computed_at":"2026-07-05T11:34:26.204147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:34:26.204147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aVjaNeYtxlh3uBRH4zLAkuhbdNAdBAo3mWJDDqrK0l+NNl8g9PIV4Fb5q5om4FTWnpaRz21QtrAwx0y2Qah7AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:34:26.204740Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.06977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89a349730c223acef67c8941df7fd4f389f91c366a205814918631183489e03c","sha256:59cad5d1de0372b80161dfedc91c2ac71eb77e98005de2ef0ad11994d0bac61f"],"state_sha256":"2718cc16e33f7d8a509e5368003cbd90bc1315f35ff8d6d05443b5a9a4572373"}