{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:SNYEPSFCMIXUHOLYHVCPMPYRLS","short_pith_number":"pith:SNYEPSFC","canonical_record":{"source":{"id":"2407.20370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-29T18:42:28Z","cross_cats_sorted":[],"title_canon_sha256":"17f52454f17adc760678d5fc0d3dac8235476d334ce1fe620c55f9bec1c7138e","abstract_canon_sha256":"29d750ab3fe051fa47f1d4e49d1b245290015177822b1105302456fa092d5659"},"schema_version":"1.0"},"canonical_sha256":"937047c8a2622f43b9783d44f63f115cba52db0251624031b8253625c008e15d","source":{"kind":"arxiv","id":"2407.20370","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.20370","created_at":"2026-07-05T08:49:57Z"},{"alias_kind":"arxiv_version","alias_value":"2407.20370v1","created_at":"2026-07-05T08:49:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.20370","created_at":"2026-07-05T08:49:57Z"},{"alias_kind":"pith_short_12","alias_value":"SNYEPSFCMIXU","created_at":"2026-07-05T08:49:57Z"},{"alias_kind":"pith_short_16","alias_value":"SNYEPSFCMIXUHOLY","created_at":"2026-07-05T08:49:57Z"},{"alias_kind":"pith_short_8","alias_value":"SNYEPSFC","created_at":"2026-07-05T08:49:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:SNYEPSFCMIXUHOLYHVCPMPYRLS","target":"record","payload":{"canonical_record":{"source":{"id":"2407.20370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-29T18:42:28Z","cross_cats_sorted":[],"title_canon_sha256":"17f52454f17adc760678d5fc0d3dac8235476d334ce1fe620c55f9bec1c7138e","abstract_canon_sha256":"29d750ab3fe051fa47f1d4e49d1b245290015177822b1105302456fa092d5659"},"schema_version":"1.0"},"canonical_sha256":"937047c8a2622f43b9783d44f63f115cba52db0251624031b8253625c008e15d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:49:57.017309Z","signature_b64":"DXkjS8JhWuLkfd49axjSidxT8veRJTvy0xdaJGzL1J0X9lU3wVS9HMECV7bKwbqf9R2+g2r+Zfj/hL8aI2qhAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"937047c8a2622f43b9783d44f63f115cba52db0251624031b8253625c008e15d","last_reissued_at":"2026-07-05T08:49:57.016788Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:49:57.016788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.20370","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":"2026-07-05T08:49:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vxNxmwJKLa20TVs7QsmLG3FuTu5s3PLHVFEt1XPkDYKI+rp5I2FFXAdPaSYrskI1oht1OSo0pmuJqfIbpgiUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:30:24.901725Z"},"content_sha256":"764e3e68007ef0e9471c17afcc3a91d695a7da172c3ca132222b70a7a12936f5","schema_version":"1.0","event_id":"sha256:764e3e68007ef0e9471c17afcc3a91d695a7da172c3ca132222b70a7a12936f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:SNYEPSFCMIXUHOLYHVCPMPYRLS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How to burn a Latin square","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anthony Bonato, Caleb Jones, Teddy Mishura, Trent G. Marbach","submitted_at":"2024-07-29T18:42:28Z","abstract_excerpt":"We investigate the lazy burning process for Latin squares by studying their associated hypergraphs. In lazy burning, a set of vertices in a hypergraph is initially burned, and that burning spreads to neighboring vertices over time via a specified propagation rule. The lazy burning number is the minimum number of initially burned vertices that eventually burns all vertices. The hypergraphs associated with Latin squares include the $n$-uniform hypergraph, whose vertices and hyperedges correspond to the entries and lines (that is, sets of rows, columns, or symbols) of the Latin square, respective"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.20370","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/2407.20370/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":"2026-07-05T08:49:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q3odc5Gfol3QVybVRyXM9KSLz06OWnYq9XzhFBde3pTLQREiKUhPU3H6XYuX1FPZuu2JMHe8SPRUFiwOO5I/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:30:24.902101Z"},"content_sha256":"e13162fb8735acb12755c7ee04c6634908f5ead41b8d1e5736d11bd9cb45a837","schema_version":"1.0","event_id":"sha256:e13162fb8735acb12755c7ee04c6634908f5ead41b8d1e5736d11bd9cb45a837"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SNYEPSFCMIXUHOLYHVCPMPYRLS/bundle.json","state_url":"https://pith.science/pith/SNYEPSFCMIXUHOLYHVCPMPYRLS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SNYEPSFCMIXUHOLYHVCPMPYRLS/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":"2026-07-06T14:30:24Z","links":{"resolver":"https://pith.science/pith/SNYEPSFCMIXUHOLYHVCPMPYRLS","bundle":"https://pith.science/pith/SNYEPSFCMIXUHOLYHVCPMPYRLS/bundle.json","state":"https://pith.science/pith/SNYEPSFCMIXUHOLYHVCPMPYRLS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SNYEPSFCMIXUHOLYHVCPMPYRLS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SNYEPSFCMIXUHOLYHVCPMPYRLS","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":"29d750ab3fe051fa47f1d4e49d1b245290015177822b1105302456fa092d5659","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-29T18:42:28Z","title_canon_sha256":"17f52454f17adc760678d5fc0d3dac8235476d334ce1fe620c55f9bec1c7138e"},"schema_version":"1.0","source":{"id":"2407.20370","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.20370","created_at":"2026-07-05T08:49:57Z"},{"alias_kind":"arxiv_version","alias_value":"2407.20370v1","created_at":"2026-07-05T08:49:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.20370","created_at":"2026-07-05T08:49:57Z"},{"alias_kind":"pith_short_12","alias_value":"SNYEPSFCMIXU","created_at":"2026-07-05T08:49:57Z"},{"alias_kind":"pith_short_16","alias_value":"SNYEPSFCMIXUHOLY","created_at":"2026-07-05T08:49:57Z"},{"alias_kind":"pith_short_8","alias_value":"SNYEPSFC","created_at":"2026-07-05T08:49:57Z"}],"graph_snapshots":[{"event_id":"sha256:e13162fb8735acb12755c7ee04c6634908f5ead41b8d1e5736d11bd9cb45a837","target":"graph","created_at":"2026-07-05T08:49:57Z","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/2407.20370/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the lazy burning process for Latin squares by studying their associated hypergraphs. In lazy burning, a set of vertices in a hypergraph is initially burned, and that burning spreads to neighboring vertices over time via a specified propagation rule. The lazy burning number is the minimum number of initially burned vertices that eventually burns all vertices. The hypergraphs associated with Latin squares include the $n$-uniform hypergraph, whose vertices and hyperedges correspond to the entries and lines (that is, sets of rows, columns, or symbols) of the Latin square, respective","authors_text":"Anthony Bonato, Caleb Jones, Teddy Mishura, Trent G. Marbach","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-29T18:42:28Z","title":"How to burn a Latin square"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.20370","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":"sha256:764e3e68007ef0e9471c17afcc3a91d695a7da172c3ca132222b70a7a12936f5","target":"record","created_at":"2026-07-05T08:49:57Z","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":"29d750ab3fe051fa47f1d4e49d1b245290015177822b1105302456fa092d5659","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-29T18:42:28Z","title_canon_sha256":"17f52454f17adc760678d5fc0d3dac8235476d334ce1fe620c55f9bec1c7138e"},"schema_version":"1.0","source":{"id":"2407.20370","kind":"arxiv","version":1}},"canonical_sha256":"937047c8a2622f43b9783d44f63f115cba52db0251624031b8253625c008e15d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"937047c8a2622f43b9783d44f63f115cba52db0251624031b8253625c008e15d","first_computed_at":"2026-07-05T08:49:57.016788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:49:57.016788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DXkjS8JhWuLkfd49axjSidxT8veRJTvy0xdaJGzL1J0X9lU3wVS9HMECV7bKwbqf9R2+g2r+Zfj/hL8aI2qhAg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:49:57.017309Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.20370","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:764e3e68007ef0e9471c17afcc3a91d695a7da172c3ca132222b70a7a12936f5","sha256:e13162fb8735acb12755c7ee04c6634908f5ead41b8d1e5736d11bd9cb45a837"],"state_sha256":"3dc856b1f9bbafb8481c2639523b5982080ce53dce8bb68edaeb191050740f38"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ORoqkG/5BcmHD67pgqERMWns/W2dX9nIalPIf81dXEFzcVkr2GlZtixmyd73HBUt6zr1tJEJMfhSdP8uLIBQAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T14:30:24.904081Z","bundle_sha256":"2b1528c05c170a4aaf98222e3dc475ebb782f00b1b27342494edb41974cdd809"}}