{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:FD75RGFXJRJOF32KTICUEOIFBV","short_pith_number":"pith:FD75RGFX","canonical_record":{"source":{"id":"2507.17913","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-23T20:23:34Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"35eb5ae6770cdd9a088cda30bbc9a6091191ebf09901e65f9bc19e200d7b922f","abstract_canon_sha256":"38d357a1f4b3143bd193797847f025280ba6461390ab43c92375399011cb565a"},"schema_version":"1.0"},"canonical_sha256":"28ffd898b74c52e2ef4a9a054239050d4739afcb9ab86ddebd934a9e146a79eb","source":{"kind":"arxiv","id":"2507.17913","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.17913","created_at":"2026-07-05T11:42:37Z"},{"alias_kind":"arxiv_version","alias_value":"2507.17913v1","created_at":"2026-07-05T11:42:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.17913","created_at":"2026-07-05T11:42:37Z"},{"alias_kind":"pith_short_12","alias_value":"FD75RGFXJRJO","created_at":"2026-07-05T11:42:37Z"},{"alias_kind":"pith_short_16","alias_value":"FD75RGFXJRJOF32K","created_at":"2026-07-05T11:42:37Z"},{"alias_kind":"pith_short_8","alias_value":"FD75RGFX","created_at":"2026-07-05T11:42:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:FD75RGFXJRJOF32KTICUEOIFBV","target":"record","payload":{"canonical_record":{"source":{"id":"2507.17913","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-23T20:23:34Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"35eb5ae6770cdd9a088cda30bbc9a6091191ebf09901e65f9bc19e200d7b922f","abstract_canon_sha256":"38d357a1f4b3143bd193797847f025280ba6461390ab43c92375399011cb565a"},"schema_version":"1.0"},"canonical_sha256":"28ffd898b74c52e2ef4a9a054239050d4739afcb9ab86ddebd934a9e146a79eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:42:37.487207Z","signature_b64":"tgTU2gWIG2iCdskQJyf28vl7EvOIfb3ryoe6e/HcBEFVtRopabfNiZWKwAGbl1jJlPrVFgKgR9xLcKi5iWpWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28ffd898b74c52e2ef4a9a054239050d4739afcb9ab86ddebd934a9e146a79eb","last_reissued_at":"2026-07-05T11:42:37.486787Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:42:37.486787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.17913","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:42:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A4vcJ7Ltjs8jPhbbC6iVlgXYcos02B7HiGGVOMZGZCxh+VwhgH5yrk75+rKKqhI5tUHXS6kocM/6tQJvYM8bBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T04:47:26.279307Z"},"content_sha256":"ace418972e97b913496b20a03fa03d3413655b6f5571a79536a41152ecffae20","schema_version":"1.0","event_id":"sha256:ace418972e97b913496b20a03fa03d3413655b6f5571a79536a41152ecffae20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:FD75RGFXJRJOF32KTICUEOIFBV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A complete $t$-intersection theorem for families of spanning trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Andrey Kupavskii, Elizaveta Iarovikova","submitted_at":"2025-07-23T20:23:34Z","abstract_excerpt":"Let $\\mathcal T_n$ denote the set of all labelled spanning trees of $K_n$. A family $\\mathcal F \\subset \\mathcal T_n$ is $t$-intersecting if for all $A, B \\in \\mathcal F$ the trees $A$ and $B$ share at least $t$ edges. In this paper, we determine for $n>n_0$ the size of the largest $t$-intersecting family $\\mathcal F\\subset \\mathcal T_n$ for all meaningful values of $t$ ($t\\le n-1$). This result is a rare instance when a complete $t$-intersection theorem for a given type of structures is known."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.17913","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.17913/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:42:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vlu0NodReFV/GTkBsNzT2XYvwYg2YNrRU0ADbu/L9xscAsTtoGJz+z8MpRQs9nf2C4xLbXhe0juHN0ON5QhxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T04:47:26.279972Z"},"content_sha256":"1ccc0a86113ff087a1b7f4fb1595d1b7a416c967bf9ac1b0c1d22c4ec750f27d","schema_version":"1.0","event_id":"sha256:1ccc0a86113ff087a1b7f4fb1595d1b7a416c967bf9ac1b0c1d22c4ec750f27d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FD75RGFXJRJOF32KTICUEOIFBV/bundle.json","state_url":"https://pith.science/pith/FD75RGFXJRJOF32KTICUEOIFBV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FD75RGFXJRJOF32KTICUEOIFBV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-07T04:47:26Z","links":{"resolver":"https://pith.science/pith/FD75RGFXJRJOF32KTICUEOIFBV","bundle":"https://pith.science/pith/FD75RGFXJRJOF32KTICUEOIFBV/bundle.json","state":"https://pith.science/pith/FD75RGFXJRJOF32KTICUEOIFBV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FD75RGFXJRJOF32KTICUEOIFBV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FD75RGFXJRJOF32KTICUEOIFBV","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":"38d357a1f4b3143bd193797847f025280ba6461390ab43c92375399011cb565a","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-23T20:23:34Z","title_canon_sha256":"35eb5ae6770cdd9a088cda30bbc9a6091191ebf09901e65f9bc19e200d7b922f"},"schema_version":"1.0","source":{"id":"2507.17913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.17913","created_at":"2026-07-05T11:42:37Z"},{"alias_kind":"arxiv_version","alias_value":"2507.17913v1","created_at":"2026-07-05T11:42:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.17913","created_at":"2026-07-05T11:42:37Z"},{"alias_kind":"pith_short_12","alias_value":"FD75RGFXJRJO","created_at":"2026-07-05T11:42:37Z"},{"alias_kind":"pith_short_16","alias_value":"FD75RGFXJRJOF32K","created_at":"2026-07-05T11:42:37Z"},{"alias_kind":"pith_short_8","alias_value":"FD75RGFX","created_at":"2026-07-05T11:42:37Z"}],"graph_snapshots":[{"event_id":"sha256:1ccc0a86113ff087a1b7f4fb1595d1b7a416c967bf9ac1b0c1d22c4ec750f27d","target":"graph","created_at":"2026-07-05T11:42:37Z","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/2507.17913/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathcal T_n$ denote the set of all labelled spanning trees of $K_n$. A family $\\mathcal F \\subset \\mathcal T_n$ is $t$-intersecting if for all $A, B \\in \\mathcal F$ the trees $A$ and $B$ share at least $t$ edges. In this paper, we determine for $n>n_0$ the size of the largest $t$-intersecting family $\\mathcal F\\subset \\mathcal T_n$ for all meaningful values of $t$ ($t\\le n-1$). This result is a rare instance when a complete $t$-intersection theorem for a given type of structures is known.","authors_text":"Andrey Kupavskii, Elizaveta Iarovikova","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-23T20:23:34Z","title":"A complete $t$-intersection theorem for families of spanning trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.17913","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:ace418972e97b913496b20a03fa03d3413655b6f5571a79536a41152ecffae20","target":"record","created_at":"2026-07-05T11:42:37Z","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":"38d357a1f4b3143bd193797847f025280ba6461390ab43c92375399011cb565a","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-23T20:23:34Z","title_canon_sha256":"35eb5ae6770cdd9a088cda30bbc9a6091191ebf09901e65f9bc19e200d7b922f"},"schema_version":"1.0","source":{"id":"2507.17913","kind":"arxiv","version":1}},"canonical_sha256":"28ffd898b74c52e2ef4a9a054239050d4739afcb9ab86ddebd934a9e146a79eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28ffd898b74c52e2ef4a9a054239050d4739afcb9ab86ddebd934a9e146a79eb","first_computed_at":"2026-07-05T11:42:37.486787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:42:37.486787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tgTU2gWIG2iCdskQJyf28vl7EvOIfb3ryoe6e/HcBEFVtRopabfNiZWKwAGbl1jJlPrVFgKgR9xLcKi5iWpWBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:42:37.487207Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.17913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ace418972e97b913496b20a03fa03d3413655b6f5571a79536a41152ecffae20","sha256:1ccc0a86113ff087a1b7f4fb1595d1b7a416c967bf9ac1b0c1d22c4ec750f27d"],"state_sha256":"d4a0dc48d687dcc47ff672b6100bb47bf3bf68a0061a9d73e5cfefa2827a16cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NuVOGsTyxwHI7YzQ1jGd7KhMAQBHZ1bVcpVw7pO+GfhuGJpJ/c5HAzV2jRZveH+3LLEquAfDt9DW0MkDXRqUCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T04:47:26.283782Z","bundle_sha256":"98639d8bec824a740e613da4298947dcf645761c92bc0c962ad0809afe6b596c"}}