{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:TTV3GUU7AESB5FNWH5VV3HO6MS","short_pith_number":"pith:TTV3GUU7","canonical_record":{"source":{"id":"math/0404533","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.MG","submitted_at":"2004-04-29T15:21:09Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"dbbe15008f3a74e9fd5725b8c45e6145984b81d871d41c103e9cddb4787fd8c0","abstract_canon_sha256":"4033d90fbce20b08cc2fe12177e2b9b7c27869316c2b0f3edf842fedf29f53d2"},"schema_version":"1.0"},"canonical_sha256":"9cebb3529f01241e95b63f6b5d9dde64a32b25083db0c66aaaf23e95baf27144","source":{"kind":"arxiv","id":"math/0404533","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0404533","created_at":"2026-07-04T14:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0404533v1","created_at":"2026-07-04T14:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0404533","created_at":"2026-07-04T14:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"TTV3GUU7AESB","created_at":"2026-07-04T14:38:34Z"},{"alias_kind":"pith_short_16","alias_value":"TTV3GUU7AESB5FNW","created_at":"2026-07-04T14:38:34Z"},{"alias_kind":"pith_short_8","alias_value":"TTV3GUU7","created_at":"2026-07-04T14:38:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:TTV3GUU7AESB5FNWH5VV3HO6MS","target":"record","payload":{"canonical_record":{"source":{"id":"math/0404533","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.MG","submitted_at":"2004-04-29T15:21:09Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"dbbe15008f3a74e9fd5725b8c45e6145984b81d871d41c103e9cddb4787fd8c0","abstract_canon_sha256":"4033d90fbce20b08cc2fe12177e2b9b7c27869316c2b0f3edf842fedf29f53d2"},"schema_version":"1.0"},"canonical_sha256":"9cebb3529f01241e95b63f6b5d9dde64a32b25083db0c66aaaf23e95baf27144","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:38:34.381821Z","signature_b64":"uul9RWgXxNX3KoUIQ5Fgl1eqhZJK+UGnLcnU9a86qjrhpQBmkaYvl1FKZ1gvcAnigV4XKNKKKr6eIklKIb+vAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cebb3529f01241e95b63f6b5d9dde64a32b25083db0c66aaaf23e95baf27144","last_reissued_at":"2026-07-04T14:38:34.381419Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:38:34.381419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0404533","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":"2026-07-04T14:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zbjTP4LrBxuPA9ZLttKbAVlaCpbWDU9TLKaenPRFj5GnE6o5DQuVodLABR7pVsZ7wurvbz2ykqGm3B8mHAdVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T05:05:52.377272Z"},"content_sha256":"e2c1dfab261f278d459baf6b25260f03495abb30fc9019aaef02eb45c13b90eb","schema_version":"1.0","event_id":"sha256:e2c1dfab261f278d459baf6b25260f03495abb30fc9019aaef02eb45c13b90eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:TTV3GUU7AESB5FNWH5VV3HO6MS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On fractal Peano curves","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.MG","authors_text":"Evgeny Shchepin","submitted_at":"2004-04-29T15:21:09Z","abstract_excerpt":"It is proved that for every fractal continuous mapping F: I\\to I^2 of the unit interval onto the unit square there is a pair of points x,y\\in I, such that |F(x)-F(y)|^2\\ge 5|x-y|."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0404533","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/math/0404533/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":"2026-07-04T14:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B6WdF0rfCPhySlIW3R5RAPjFDZFvCckjrXVe8xXzDTmkBcJtiuHU7mg+G1Q4CwXzz+WGwSjZCnO+b3UMmEpJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T05:05:52.377663Z"},"content_sha256":"84ec65949c10a9bc17d53be2c9f60099de81ca4d3b4a3adeb371fabeda444735","schema_version":"1.0","event_id":"sha256:84ec65949c10a9bc17d53be2c9f60099de81ca4d3b4a3adeb371fabeda444735"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TTV3GUU7AESB5FNWH5VV3HO6MS/bundle.json","state_url":"https://pith.science/pith/TTV3GUU7AESB5FNWH5VV3HO6MS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TTV3GUU7AESB5FNWH5VV3HO6MS/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":"2026-07-09T05:05:52Z","links":{"resolver":"https://pith.science/pith/TTV3GUU7AESB5FNWH5VV3HO6MS","bundle":"https://pith.science/pith/TTV3GUU7AESB5FNWH5VV3HO6MS/bundle.json","state":"https://pith.science/pith/TTV3GUU7AESB5FNWH5VV3HO6MS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TTV3GUU7AESB5FNWH5VV3HO6MS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:TTV3GUU7AESB5FNWH5VV3HO6MS","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":"4033d90fbce20b08cc2fe12177e2b9b7c27869316c2b0f3edf842fedf29f53d2","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.MG","submitted_at":"2004-04-29T15:21:09Z","title_canon_sha256":"dbbe15008f3a74e9fd5725b8c45e6145984b81d871d41c103e9cddb4787fd8c0"},"schema_version":"1.0","source":{"id":"math/0404533","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0404533","created_at":"2026-07-04T14:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0404533v1","created_at":"2026-07-04T14:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0404533","created_at":"2026-07-04T14:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"TTV3GUU7AESB","created_at":"2026-07-04T14:38:34Z"},{"alias_kind":"pith_short_16","alias_value":"TTV3GUU7AESB5FNW","created_at":"2026-07-04T14:38:34Z"},{"alias_kind":"pith_short_8","alias_value":"TTV3GUU7","created_at":"2026-07-04T14:38:34Z"}],"graph_snapshots":[{"event_id":"sha256:84ec65949c10a9bc17d53be2c9f60099de81ca4d3b4a3adeb371fabeda444735","target":"graph","created_at":"2026-07-04T14:38:34Z","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/math/0404533/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is proved that for every fractal continuous mapping F: I\\to I^2 of the unit interval onto the unit square there is a pair of points x,y\\in I, such that |F(x)-F(y)|^2\\ge 5|x-y|.","authors_text":"Evgeny Shchepin","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.MG","submitted_at":"2004-04-29T15:21:09Z","title":"On fractal Peano curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0404533","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:e2c1dfab261f278d459baf6b25260f03495abb30fc9019aaef02eb45c13b90eb","target":"record","created_at":"2026-07-04T14:38:34Z","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":"4033d90fbce20b08cc2fe12177e2b9b7c27869316c2b0f3edf842fedf29f53d2","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.MG","submitted_at":"2004-04-29T15:21:09Z","title_canon_sha256":"dbbe15008f3a74e9fd5725b8c45e6145984b81d871d41c103e9cddb4787fd8c0"},"schema_version":"1.0","source":{"id":"math/0404533","kind":"arxiv","version":1}},"canonical_sha256":"9cebb3529f01241e95b63f6b5d9dde64a32b25083db0c66aaaf23e95baf27144","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cebb3529f01241e95b63f6b5d9dde64a32b25083db0c66aaaf23e95baf27144","first_computed_at":"2026-07-04T14:38:34.381419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:38:34.381419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uul9RWgXxNX3KoUIQ5Fgl1eqhZJK+UGnLcnU9a86qjrhpQBmkaYvl1FKZ1gvcAnigV4XKNKKKr6eIklKIb+vAA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:38:34.381821Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0404533","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2c1dfab261f278d459baf6b25260f03495abb30fc9019aaef02eb45c13b90eb","sha256:84ec65949c10a9bc17d53be2c9f60099de81ca4d3b4a3adeb371fabeda444735"],"state_sha256":"a87562736e83c7a0c5b2d7d7b8d522455e5df67307e1447eba22432e0cb2eee4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ty3T8NN/01d3MlbAy0z6SETNzBjlpSxnmXQTMcJ/L/1YpG93jAMET1I4+kBaEDJbQELgsyb+WVe0KyXsACG8Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T05:05:52.379644Z","bundle_sha256":"3e0afa7aaeb2e3686b86564e6c3ec312e1b0f0a08ff3ad02d0ab1ab8d8213461"}}