{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:WF436HHCVQNJCXNLRGLE6LRZA6","short_pith_number":"pith:WF436HHC","canonical_record":{"source":{"id":"2506.07147","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-08T13:50:57Z","cross_cats_sorted":[],"title_canon_sha256":"7d172974b2846ac7b80d0cae6287e6c45520e121a14a8c758b7942e2bc8e0a32","abstract_canon_sha256":"f35c44a0043866ae327c48512bcd19fa9f0b8fb40925ed37ac9402f60dbb44cb"},"schema_version":"1.0"},"canonical_sha256":"b179bf1ce2ac1a915dab89964f2e3907964ff575260e5f361d4e770665175f73","source":{"kind":"arxiv","id":"2506.07147","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07147","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07147v1","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07147","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"pith_short_12","alias_value":"WF436HHCVQNJ","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"pith_short_16","alias_value":"WF436HHCVQNJCXNL","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"pith_short_8","alias_value":"WF436HHC","created_at":"2026-07-05T11:18:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:WF436HHCVQNJCXNLRGLE6LRZA6","target":"record","payload":{"canonical_record":{"source":{"id":"2506.07147","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-08T13:50:57Z","cross_cats_sorted":[],"title_canon_sha256":"7d172974b2846ac7b80d0cae6287e6c45520e121a14a8c758b7942e2bc8e0a32","abstract_canon_sha256":"f35c44a0043866ae327c48512bcd19fa9f0b8fb40925ed37ac9402f60dbb44cb"},"schema_version":"1.0"},"canonical_sha256":"b179bf1ce2ac1a915dab89964f2e3907964ff575260e5f361d4e770665175f73","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:02.457080Z","signature_b64":"Pk8jae8RBHudAQT+DWfYIAUQU+wg8NWhBdQ9UAcVmWYKCQHooEatcG9ulfmDdWOjbe5mzM+ZBngJW74YxaPWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b179bf1ce2ac1a915dab89964f2e3907964ff575260e5f361d4e770665175f73","last_reissued_at":"2026-07-05T11:18:02.456603Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:02.456603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.07147","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":"2026-07-05T11:18:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v/iWQ6U/WtDGt/9KCaDhR+4r4UE0wT7qraTVVyd7v89nrUd3eX7dZ1Z3fLxzEElNWOItq0LPbHIY9P5JwwnkBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T02:14:20.205403Z"},"content_sha256":"9e866212c1764171b7368c518d3f39d2a523d62acbe50eaf89aa6df24cf2c46a","schema_version":"1.0","event_id":"sha256:9e866212c1764171b7368c518d3f39d2a523d62acbe50eaf89aa6df24cf2c46a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:WF436HHCVQNJCXNLRGLE6LRZA6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Packing tetrahedrons in edge-weighted graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Donglei Yang, Shunan Wei, Wanting Sun","submitted_at":"2025-06-08T13:50:57Z","abstract_excerpt":"We prove that for all $\\mu>0, t\\in (0,1)$ and sufficiently large $n\\in 4\\mathbb{N}$, if $G$ is an edge-weighted complete graph on $n$ vertices with a weight function $w: E(G)\\rightarrow [0,1]$ and the minimum weighted degree $\\delta^w(G)\\geq (\\tfrac{1+3t}{4}+\\mu)n$, then $G$ contains a $K_4$-factor where each copy of $K_4$ has total weight more than $6t$. This confirms a conjecture of Balogh--Kemkes--Lee--Young for the tetrahedron case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07147","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/2506.07147/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":"2026-07-05T11:18:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6rJvnyA0gTKRxTnX/IlYjwfQqZic5vo8Fvf3r3PkOb0hOPq0HpnBYYoSW/jiQJoneiWvZ0miTXC4BBtfTZt1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T02:14:20.205908Z"},"content_sha256":"fe2c8512937c728704e7886c2863bec60d4dbf115677e3269d1afba32c13faf5","schema_version":"1.0","event_id":"sha256:fe2c8512937c728704e7886c2863bec60d4dbf115677e3269d1afba32c13faf5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WF436HHCVQNJCXNLRGLE6LRZA6/bundle.json","state_url":"https://pith.science/pith/WF436HHCVQNJCXNLRGLE6LRZA6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WF436HHCVQNJCXNLRGLE6LRZA6/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":"2026-08-08T02:14:20Z","links":{"resolver":"https://pith.science/pith/WF436HHCVQNJCXNLRGLE6LRZA6","bundle":"https://pith.science/pith/WF436HHCVQNJCXNLRGLE6LRZA6/bundle.json","state":"https://pith.science/pith/WF436HHCVQNJCXNLRGLE6LRZA6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WF436HHCVQNJCXNLRGLE6LRZA6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WF436HHCVQNJCXNLRGLE6LRZA6","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":"f35c44a0043866ae327c48512bcd19fa9f0b8fb40925ed37ac9402f60dbb44cb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-08T13:50:57Z","title_canon_sha256":"7d172974b2846ac7b80d0cae6287e6c45520e121a14a8c758b7942e2bc8e0a32"},"schema_version":"1.0","source":{"id":"2506.07147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07147","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07147v1","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07147","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"pith_short_12","alias_value":"WF436HHCVQNJ","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"pith_short_16","alias_value":"WF436HHCVQNJCXNL","created_at":"2026-07-05T11:18:02Z"},{"alias_kind":"pith_short_8","alias_value":"WF436HHC","created_at":"2026-07-05T11:18:02Z"}],"graph_snapshots":[{"event_id":"sha256:fe2c8512937c728704e7886c2863bec60d4dbf115677e3269d1afba32c13faf5","target":"graph","created_at":"2026-07-05T11:18:02Z","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/2506.07147/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that for all $\\mu>0, t\\in (0,1)$ and sufficiently large $n\\in 4\\mathbb{N}$, if $G$ is an edge-weighted complete graph on $n$ vertices with a weight function $w: E(G)\\rightarrow [0,1]$ and the minimum weighted degree $\\delta^w(G)\\geq (\\tfrac{1+3t}{4}+\\mu)n$, then $G$ contains a $K_4$-factor where each copy of $K_4$ has total weight more than $6t$. This confirms a conjecture of Balogh--Kemkes--Lee--Young for the tetrahedron case.","authors_text":"Donglei Yang, Shunan Wei, Wanting Sun","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-08T13:50:57Z","title":"Packing tetrahedrons in edge-weighted graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07147","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":"sha256:9e866212c1764171b7368c518d3f39d2a523d62acbe50eaf89aa6df24cf2c46a","target":"record","created_at":"2026-07-05T11:18:02Z","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":"f35c44a0043866ae327c48512bcd19fa9f0b8fb40925ed37ac9402f60dbb44cb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-08T13:50:57Z","title_canon_sha256":"7d172974b2846ac7b80d0cae6287e6c45520e121a14a8c758b7942e2bc8e0a32"},"schema_version":"1.0","source":{"id":"2506.07147","kind":"arxiv","version":1}},"canonical_sha256":"b179bf1ce2ac1a915dab89964f2e3907964ff575260e5f361d4e770665175f73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b179bf1ce2ac1a915dab89964f2e3907964ff575260e5f361d4e770665175f73","first_computed_at":"2026-07-05T11:18:02.456603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:18:02.456603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pk8jae8RBHudAQT+DWfYIAUQU+wg8NWhBdQ9UAcVmWYKCQHooEatcG9ulfmDdWOjbe5mzM+ZBngJW74YxaPWCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:18:02.457080Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.07147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e866212c1764171b7368c518d3f39d2a523d62acbe50eaf89aa6df24cf2c46a","sha256:fe2c8512937c728704e7886c2863bec60d4dbf115677e3269d1afba32c13faf5"],"state_sha256":"44e3603657f8acbbba0ab79ee9e917745fc454e884eb13d171b64c6c506005bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tSM9KlE71CFeIAoO7r9yWKBIFEnN1AGFRb6H5lMaJrsPUHwKOMsIYej3xEA4hLMyBwQ/mWDIhcXk6fdi8ODCCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T02:14:20.209546Z","bundle_sha256":"8fa36e6f5f9479d419e94f18ec4d874bfa27c8b8567a4ce4e3a96e04788340b0"}}