{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:Z27XDSXEC6VLVB7D7KHRB7IP22","short_pith_number":"pith:Z27XDSXE","canonical_record":{"source":{"id":"2607.28793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-30T19:41:51Z","cross_cats_sorted":[],"title_canon_sha256":"356cfd8facbb8da621270192144c9f1e7bd05b4664bf3b91fee6d31eae052a55","abstract_canon_sha256":"dad573cd3241d9534554767bde87385473288ea84c3cfa2f20281f352e9db97b"},"schema_version":"1.0"},"canonical_sha256":"cebf71cae417aaba87e3fa8f10fd0fd6a4c5ffbd8cc3ef4130e3a9247a1112e6","source":{"kind":"arxiv","id":"2607.28793","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28793","created_at":"2026-08-03T00:12:53Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28793v1","created_at":"2026-08-03T00:12:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28793","created_at":"2026-08-03T00:12:53Z"},{"alias_kind":"pith_short_12","alias_value":"Z27XDSXEC6VL","created_at":"2026-08-03T00:12:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z27XDSXEC6VLVB7D","created_at":"2026-08-03T00:12:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z27XDSXE","created_at":"2026-08-03T00:12:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:Z27XDSXEC6VLVB7D7KHRB7IP22","target":"record","payload":{"canonical_record":{"source":{"id":"2607.28793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-30T19:41:51Z","cross_cats_sorted":[],"title_canon_sha256":"356cfd8facbb8da621270192144c9f1e7bd05b4664bf3b91fee6d31eae052a55","abstract_canon_sha256":"dad573cd3241d9534554767bde87385473288ea84c3cfa2f20281f352e9db97b"},"schema_version":"1.0"},"canonical_sha256":"cebf71cae417aaba87e3fa8f10fd0fd6a4c5ffbd8cc3ef4130e3a9247a1112e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-03T00:12:53.797145Z","signature_b64":"d5J8EYWIYRMXTrMjIhfiZZxp3QuUZWGXvbjfcfgV3Yq1CjMVIGULJ7J3HgAGQ6Bpok47I4WWn260jLYqt7G9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cebf71cae417aaba87e3fa8f10fd0fd6a4c5ffbd8cc3ef4130e3a9247a1112e6","last_reissued_at":"2026-08-03T00:12:53.794778Z","signature_status":"signed_v1","first_computed_at":"2026-08-03T00:12:53.794778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.28793","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":"2026-08-03T00:12:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KPHe7Urw2/aRXgt3mV//yjVyd1lfF9XIAGspmrAm2xOOZMC/u2NRan+smK+ENWfUmfdnrNJW2b2/3Yx2WwirBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T18:36:08.138917Z"},"content_sha256":"1ecc77ae9f33cf9f09f9c442ef7c94c1fcc2c9ec5579b44a6a7197f8a8d932b6","schema_version":"1.0","event_id":"sha256:1ecc77ae9f33cf9f09f9c442ef7c94c1fcc2c9ec5579b44a6a7197f8a8d932b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:Z27XDSXEC6VLVB7D7KHRB7IP22","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Favard length and generalized projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alex McDonald, Izabella Laba, Krystal Taylor","submitted_at":"2026-07-30T19:41:51Z","abstract_excerpt":"We investigate generalized Favard lengths associated to smooth families of nonlinear projections. Under suitable regularity and transversality assumptions, we prove that generalized projections are locally comparable to orthogonal projections on sufficiently small scales. This yields a comparison principle that transfers quantitative upper bounds for classical Favard length to broad classes of nonlinear projection families.\n  As a consequence, known upper bounds for the Favard length of purely unrectifiable self-similar 1-sets yield corresponding upper bounds for their generalized Favard lengt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28793","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/2607.28793/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":"2026-08-03T00:12:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XV89om/ortJzNXRbKqnp8bLzAj/yARygvUTjOWWpHVM7RC63f5yvgZlZh8kzcNt0NPF4GwKosVmVkDZmBMx6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T18:36:08.139837Z"},"content_sha256":"8bb90566811962754705b6fe530154ce1ecf618192fcdb9124d29f0ad54641cb","schema_version":"1.0","event_id":"sha256:8bb90566811962754705b6fe530154ce1ecf618192fcdb9124d29f0ad54641cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z27XDSXEC6VLVB7D7KHRB7IP22/bundle.json","state_url":"https://pith.science/pith/Z27XDSXEC6VLVB7D7KHRB7IP22/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z27XDSXEC6VLVB7D7KHRB7IP22/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":"2026-08-15T18:36:08Z","links":{"resolver":"https://pith.science/pith/Z27XDSXEC6VLVB7D7KHRB7IP22","bundle":"https://pith.science/pith/Z27XDSXEC6VLVB7D7KHRB7IP22/bundle.json","state":"https://pith.science/pith/Z27XDSXEC6VLVB7D7KHRB7IP22/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z27XDSXEC6VLVB7D7KHRB7IP22/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Z27XDSXEC6VLVB7D7KHRB7IP22","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":"dad573cd3241d9534554767bde87385473288ea84c3cfa2f20281f352e9db97b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-30T19:41:51Z","title_canon_sha256":"356cfd8facbb8da621270192144c9f1e7bd05b4664bf3b91fee6d31eae052a55"},"schema_version":"1.0","source":{"id":"2607.28793","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28793","created_at":"2026-08-03T00:12:53Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28793v1","created_at":"2026-08-03T00:12:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28793","created_at":"2026-08-03T00:12:53Z"},{"alias_kind":"pith_short_12","alias_value":"Z27XDSXEC6VL","created_at":"2026-08-03T00:12:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z27XDSXEC6VLVB7D","created_at":"2026-08-03T00:12:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z27XDSXE","created_at":"2026-08-03T00:12:53Z"}],"graph_snapshots":[{"event_id":"sha256:8bb90566811962754705b6fe530154ce1ecf618192fcdb9124d29f0ad54641cb","target":"graph","created_at":"2026-08-03T00:12:53Z","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/2607.28793/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate generalized Favard lengths associated to smooth families of nonlinear projections. Under suitable regularity and transversality assumptions, we prove that generalized projections are locally comparable to orthogonal projections on sufficiently small scales. This yields a comparison principle that transfers quantitative upper bounds for classical Favard length to broad classes of nonlinear projection families.\n  As a consequence, known upper bounds for the Favard length of purely unrectifiable self-similar 1-sets yield corresponding upper bounds for their generalized Favard lengt","authors_text":"Alex McDonald, Izabella Laba, Krystal Taylor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-30T19:41:51Z","title":"Favard length and generalized projections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28793","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":"sha256:1ecc77ae9f33cf9f09f9c442ef7c94c1fcc2c9ec5579b44a6a7197f8a8d932b6","target":"record","created_at":"2026-08-03T00:12:53Z","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":"dad573cd3241d9534554767bde87385473288ea84c3cfa2f20281f352e9db97b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-30T19:41:51Z","title_canon_sha256":"356cfd8facbb8da621270192144c9f1e7bd05b4664bf3b91fee6d31eae052a55"},"schema_version":"1.0","source":{"id":"2607.28793","kind":"arxiv","version":1}},"canonical_sha256":"cebf71cae417aaba87e3fa8f10fd0fd6a4c5ffbd8cc3ef4130e3a9247a1112e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cebf71cae417aaba87e3fa8f10fd0fd6a4c5ffbd8cc3ef4130e3a9247a1112e6","first_computed_at":"2026-08-03T00:12:53.794778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T00:12:53.794778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d5J8EYWIYRMXTrMjIhfiZZxp3QuUZWGXvbjfcfgV3Yq1CjMVIGULJ7J3HgAGQ6Bpok47I4WWn260jLYqt7G9Dg==","signature_status":"signed_v1","signed_at":"2026-08-03T00:12:53.797145Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.28793","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ecc77ae9f33cf9f09f9c442ef7c94c1fcc2c9ec5579b44a6a7197f8a8d932b6","sha256:8bb90566811962754705b6fe530154ce1ecf618192fcdb9124d29f0ad54641cb"],"state_sha256":"344f6fb0263d9de25865fc449a14d228de43b2877d5b72d8a3bb5d00a00db08c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AwCijnP1fVHOIhXM0t+UNFFS+dT7R3LtXCIRMKTE0ZDKb+cNyExznUgLvGbGnaIdY2tuX/fMSoiYJPihsN4rDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T18:36:08.148181Z","bundle_sha256":"6bdd3728fa4d922f09740bb8d773a3ef15347c4b0dde62b3a0dedc84e2049bd4"}}