{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:5PAJTRPJFWJC6VDGD7NNB6TL7H","short_pith_number":"pith:5PAJTRPJ","canonical_record":{"source":{"id":"2608.10272","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-08-10T22:12:32Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"42589f3829ada10bea7d3a3de74b2e1169cb3a55a9abd9e42922bfd09aa479b5","abstract_canon_sha256":"7ab3c93b099c7ae3d5c05a4268ef570401c6d8b10d9e29d700fffbb11b31917a"},"schema_version":"1.0"},"canonical_sha256":"ebc099c5e92d922f54661fdad0fa6bf9f88ecfa2271a501c16587fddf126fdc0","source":{"kind":"arxiv","id":"2608.10272","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.10272","created_at":"2026-08-12T00:23:14Z"},{"alias_kind":"arxiv_version","alias_value":"2608.10272v1","created_at":"2026-08-12T00:23:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.10272","created_at":"2026-08-12T00:23:14Z"},{"alias_kind":"pith_short_12","alias_value":"5PAJTRPJFWJC","created_at":"2026-08-12T00:23:14Z"},{"alias_kind":"pith_short_16","alias_value":"5PAJTRPJFWJC6VDG","created_at":"2026-08-12T00:23:14Z"},{"alias_kind":"pith_short_8","alias_value":"5PAJTRPJ","created_at":"2026-08-12T00:23:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:5PAJTRPJFWJC6VDGD7NNB6TL7H","target":"record","payload":{"canonical_record":{"source":{"id":"2608.10272","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-08-10T22:12:32Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"42589f3829ada10bea7d3a3de74b2e1169cb3a55a9abd9e42922bfd09aa479b5","abstract_canon_sha256":"7ab3c93b099c7ae3d5c05a4268ef570401c6d8b10d9e29d700fffbb11b31917a"},"schema_version":"1.0"},"canonical_sha256":"ebc099c5e92d922f54661fdad0fa6bf9f88ecfa2271a501c16587fddf126fdc0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-12T00:23:14.283232Z","signature_b64":"LBGTgjH9StZw2qID2qBooabULSydD8ua/CHswAfe/L/2CMIb4ayaow47VeQfnghLJp8QENb5/YwYBshpB4YnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebc099c5e92d922f54661fdad0fa6bf9f88ecfa2271a501c16587fddf126fdc0","last_reissued_at":"2026-08-12T00:23:14.281412Z","signature_status":"signed_v1","first_computed_at":"2026-08-12T00:23:14.281412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.10272","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":"2026-08-12T00:23:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u2kZCbv12KtXXxfXeqJ97zHc92lNzGma9p0dnMs+EvlkV6VQNvh1O3SPLiYypeT/3ePCwNg2mfczlRAoEVtaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T01:55:57.892669Z"},"content_sha256":"6402516c597557d6168bb22f7771a809273067073cf78331b7b707d6a317f31a","schema_version":"1.0","event_id":"sha256:6402516c597557d6168bb22f7771a809273067073cf78331b7b707d6a317f31a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:5PAJTRPJFWJC6VDGD7NNB6TL7H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Introduction to Universal Equations and Characteristic-free Resolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Yi Hu","submitted_at":"2026-08-10T22:12:32Z","abstract_excerpt":"Recently, we announced a proof of a characteristic-free resolution of singularities. This is a survey article on the proof. We motivate the approach, describe the new ideas, and introduce the proof in the work."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10272","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/2608.10272/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":"2026-08-12T00:23:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2zBEKegO8XUhUhdAk4Lj2fL+xo046Ff5v9OUX/V8R3dZxdHbfokYoJC4M/OcDOwSLW0SYkdjftSkk3FkEa9BAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T01:55:57.893274Z"},"content_sha256":"5b0e0f7aff5152947bf5b2bcaec94a01b5bc3596e9e5399a8011ffbf5348a2a2","schema_version":"1.0","event_id":"sha256:5b0e0f7aff5152947bf5b2bcaec94a01b5bc3596e9e5399a8011ffbf5348a2a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5PAJTRPJFWJC6VDGD7NNB6TL7H/bundle.json","state_url":"https://pith.science/pith/5PAJTRPJFWJC6VDGD7NNB6TL7H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5PAJTRPJFWJC6VDGD7NNB6TL7H/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":"2026-08-18T01:55:57Z","links":{"resolver":"https://pith.science/pith/5PAJTRPJFWJC6VDGD7NNB6TL7H","bundle":"https://pith.science/pith/5PAJTRPJFWJC6VDGD7NNB6TL7H/bundle.json","state":"https://pith.science/pith/5PAJTRPJFWJC6VDGD7NNB6TL7H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5PAJTRPJFWJC6VDGD7NNB6TL7H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5PAJTRPJFWJC6VDGD7NNB6TL7H","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":"7ab3c93b099c7ae3d5c05a4268ef570401c6d8b10d9e29d700fffbb11b31917a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-08-10T22:12:32Z","title_canon_sha256":"42589f3829ada10bea7d3a3de74b2e1169cb3a55a9abd9e42922bfd09aa479b5"},"schema_version":"1.0","source":{"id":"2608.10272","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.10272","created_at":"2026-08-12T00:23:14Z"},{"alias_kind":"arxiv_version","alias_value":"2608.10272v1","created_at":"2026-08-12T00:23:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.10272","created_at":"2026-08-12T00:23:14Z"},{"alias_kind":"pith_short_12","alias_value":"5PAJTRPJFWJC","created_at":"2026-08-12T00:23:14Z"},{"alias_kind":"pith_short_16","alias_value":"5PAJTRPJFWJC6VDG","created_at":"2026-08-12T00:23:14Z"},{"alias_kind":"pith_short_8","alias_value":"5PAJTRPJ","created_at":"2026-08-12T00:23:14Z"}],"graph_snapshots":[{"event_id":"sha256:5b0e0f7aff5152947bf5b2bcaec94a01b5bc3596e9e5399a8011ffbf5348a2a2","target":"graph","created_at":"2026-08-12T00:23:14Z","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/2608.10272/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, we announced a proof of a characteristic-free resolution of singularities. This is a survey article on the proof. We motivate the approach, describe the new ideas, and introduce the proof in the work.","authors_text":"Yi Hu","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-08-10T22:12:32Z","title":"Introduction to Universal Equations and Characteristic-free Resolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10272","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":"sha256:6402516c597557d6168bb22f7771a809273067073cf78331b7b707d6a317f31a","target":"record","created_at":"2026-08-12T00:23:14Z","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":"7ab3c93b099c7ae3d5c05a4268ef570401c6d8b10d9e29d700fffbb11b31917a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-08-10T22:12:32Z","title_canon_sha256":"42589f3829ada10bea7d3a3de74b2e1169cb3a55a9abd9e42922bfd09aa479b5"},"schema_version":"1.0","source":{"id":"2608.10272","kind":"arxiv","version":1}},"canonical_sha256":"ebc099c5e92d922f54661fdad0fa6bf9f88ecfa2271a501c16587fddf126fdc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebc099c5e92d922f54661fdad0fa6bf9f88ecfa2271a501c16587fddf126fdc0","first_computed_at":"2026-08-12T00:23:14.281412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-12T00:23:14.281412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LBGTgjH9StZw2qID2qBooabULSydD8ua/CHswAfe/L/2CMIb4ayaow47VeQfnghLJp8QENb5/YwYBshpB4YnCw==","signature_status":"signed_v1","signed_at":"2026-08-12T00:23:14.283232Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.10272","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6402516c597557d6168bb22f7771a809273067073cf78331b7b707d6a317f31a","sha256:5b0e0f7aff5152947bf5b2bcaec94a01b5bc3596e9e5399a8011ffbf5348a2a2"],"state_sha256":"54454e89e6c3fae0879d3fe5cada69e6239cea7a18aa7c3880d5e808bfe68fe5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u+duouf99URm2eYEM/77jzEPHzfV+CW9YPXnrYA4dtpIJg4oyiOi0/+cJd/CfOsCBRyLhNbcFgWEsiJppSRhDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T01:55:57.899279Z","bundle_sha256":"66813678d046822af7fcb019084e979608d529cf9d5d6b44e91802655dad5e2f"}}