{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:66Z3ZLTDKP2EQWBPYZP6523C6I","short_pith_number":"pith:66Z3ZLTD","canonical_record":{"source":{"id":"1209.3168","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-14T12:30:02Z","cross_cats_sorted":["math.GN","math.MG"],"title_canon_sha256":"9403baabfe08a3a8ee11cc4d6b61b1c7e0f0b667e5387542c631ff2d8629e91f","abstract_canon_sha256":"c53bba3afce99489addf8b015345deba6d69eabf78bfad4b41e234dbdb21484e"},"schema_version":"1.0"},"canonical_sha256":"f7b3bcae6353f448582fc65feeeb62f22e3dac5e202a3b7a486e9f60784c7962","source":{"kind":"arxiv","id":"1209.3168","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3168","created_at":"2026-05-17T23:43:57Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3168v2","created_at":"2026-05-17T23:43:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3168","created_at":"2026-05-17T23:43:57Z"},{"alias_kind":"pith_short_12","alias_value":"66Z3ZLTDKP2E","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"66Z3ZLTDKP2EQWBP","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"66Z3ZLTD","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:66Z3ZLTDKP2EQWBPYZP6523C6I","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3168","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-14T12:30:02Z","cross_cats_sorted":["math.GN","math.MG"],"title_canon_sha256":"9403baabfe08a3a8ee11cc4d6b61b1c7e0f0b667e5387542c631ff2d8629e91f","abstract_canon_sha256":"c53bba3afce99489addf8b015345deba6d69eabf78bfad4b41e234dbdb21484e"},"schema_version":"1.0"},"canonical_sha256":"f7b3bcae6353f448582fc65feeeb62f22e3dac5e202a3b7a486e9f60784c7962","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:57.119799Z","signature_b64":"cYvwq0BIfnIFAK/q6Nxjk+tkXyIQ4DHVVBSTCmGNtFAaQACrc2sEcBWDgjL/EgrjBMd2kofiUFQCqZ4wUPaIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7b3bcae6353f448582fc65feeeb62f22e3dac5e202a3b7a486e9f60784c7962","last_reissued_at":"2026-05-17T23:43:57.119062Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:57.119062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3168","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:43:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ifr8INluzaTyX4WcIFKHkoGxPp98RmgMWWU/tVxntImhwU/eYqaq2+T7aB1gID6JkcY9yUTyCcHt5a/DP7jOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:56:04.031331Z"},"content_sha256":"e774955e0dfd2186c6a84d00a32e8385c51f1bae8a9667230aae52a3af64f380","schema_version":"1.0","event_id":"sha256:e774955e0dfd2186c6a84d00a32e8385c51f1bae8a9667230aae52a3af64f380"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:66Z3ZLTDKP2EQWBPYZP6523C6I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimension and measure for generic continuous images","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.MG"],"primary_cat":"math.CA","authors_text":"\\'Abel Farkas, James T. Hyde, Jonathan M. Fraser, Rich\\'ard Balka","submitted_at":"2012-09-14T12:30:02Z","abstract_excerpt":"We consider the Banach space consisting of continuous functions from an arbitrary uncountable compact metric space, $X$, into $\\mathbb{R}^n$. The key question is `what is the generic dimension of $f(X)$?' and we consider two different approaches to answering it: Baire category and prevalence. In the Baire category setting we prove that typically the packing and upper box dimensions are as large as possible, $n$, but find that the behaviour of the Hausdorff, lower box and topological dimensions is considerably more subtle. In fact, they are typically equal to the minimum of $n$ and the topologi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3168","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-17T23:43:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MnG1yyQVtxH6r4/jmKWA9ZVT4DWtiad1Ogdv4zJ495RQ0ZRM0bQYDSO5lboRLQUZXg/fJMwKGlK/Nr0ZMD4BCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:56:04.031887Z"},"content_sha256":"82873acfe3aa189b3fd6d47d04837eb1afa0406ac1cbb147a20c2e703f0e4676","schema_version":"1.0","event_id":"sha256:82873acfe3aa189b3fd6d47d04837eb1afa0406ac1cbb147a20c2e703f0e4676"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/66Z3ZLTDKP2EQWBPYZP6523C6I/bundle.json","state_url":"https://pith.science/pith/66Z3ZLTDKP2EQWBPYZP6523C6I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/66Z3ZLTDKP2EQWBPYZP6523C6I/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":"2026-06-22T22:56:04Z","links":{"resolver":"https://pith.science/pith/66Z3ZLTDKP2EQWBPYZP6523C6I","bundle":"https://pith.science/pith/66Z3ZLTDKP2EQWBPYZP6523C6I/bundle.json","state":"https://pith.science/pith/66Z3ZLTDKP2EQWBPYZP6523C6I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/66Z3ZLTDKP2EQWBPYZP6523C6I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:66Z3ZLTDKP2EQWBPYZP6523C6I","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":"c53bba3afce99489addf8b015345deba6d69eabf78bfad4b41e234dbdb21484e","cross_cats_sorted":["math.GN","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-14T12:30:02Z","title_canon_sha256":"9403baabfe08a3a8ee11cc4d6b61b1c7e0f0b667e5387542c631ff2d8629e91f"},"schema_version":"1.0","source":{"id":"1209.3168","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3168","created_at":"2026-05-17T23:43:57Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3168v2","created_at":"2026-05-17T23:43:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3168","created_at":"2026-05-17T23:43:57Z"},{"alias_kind":"pith_short_12","alias_value":"66Z3ZLTDKP2E","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"66Z3ZLTDKP2EQWBP","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"66Z3ZLTD","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:82873acfe3aa189b3fd6d47d04837eb1afa0406ac1cbb147a20c2e703f0e4676","target":"graph","created_at":"2026-05-17T23:43:57Z","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"},"paper":{"abstract_excerpt":"We consider the Banach space consisting of continuous functions from an arbitrary uncountable compact metric space, $X$, into $\\mathbb{R}^n$. The key question is `what is the generic dimension of $f(X)$?' and we consider two different approaches to answering it: Baire category and prevalence. In the Baire category setting we prove that typically the packing and upper box dimensions are as large as possible, $n$, but find that the behaviour of the Hausdorff, lower box and topological dimensions is considerably more subtle. In fact, they are typically equal to the minimum of $n$ and the topologi","authors_text":"\\'Abel Farkas, James T. Hyde, Jonathan M. Fraser, Rich\\'ard Balka","cross_cats":["math.GN","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-14T12:30:02Z","title":"Dimension and measure for generic continuous images"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3168","kind":"arxiv","version":2},"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:e774955e0dfd2186c6a84d00a32e8385c51f1bae8a9667230aae52a3af64f380","target":"record","created_at":"2026-05-17T23:43:57Z","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":"c53bba3afce99489addf8b015345deba6d69eabf78bfad4b41e234dbdb21484e","cross_cats_sorted":["math.GN","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-09-14T12:30:02Z","title_canon_sha256":"9403baabfe08a3a8ee11cc4d6b61b1c7e0f0b667e5387542c631ff2d8629e91f"},"schema_version":"1.0","source":{"id":"1209.3168","kind":"arxiv","version":2}},"canonical_sha256":"f7b3bcae6353f448582fc65feeeb62f22e3dac5e202a3b7a486e9f60784c7962","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7b3bcae6353f448582fc65feeeb62f22e3dac5e202a3b7a486e9f60784c7962","first_computed_at":"2026-05-17T23:43:57.119062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:57.119062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cYvwq0BIfnIFAK/q6Nxjk+tkXyIQ4DHVVBSTCmGNtFAaQACrc2sEcBWDgjL/EgrjBMd2kofiUFQCqZ4wUPaIBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:57.119799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3168","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e774955e0dfd2186c6a84d00a32e8385c51f1bae8a9667230aae52a3af64f380","sha256:82873acfe3aa189b3fd6d47d04837eb1afa0406ac1cbb147a20c2e703f0e4676"],"state_sha256":"53346acfc7064c22ce7f592e1a6a4abe76a5ebb5316c45ac9d312f0a432d439e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CM2Vs1Oqsw5ALWcWbM5z4zvL1FjoPEZUWnvT3InvZpDmYaI9ynllUZ/cTyv65ClVe8xerFRMpd7L7w7MLNbwBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:56:04.034496Z","bundle_sha256":"63937f2c82d7dde27b0e0c9c9f7ce8dee6e041230e34100c1efcfc4a47273588"}}