{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:5PNF5P4L7GYLJ6NGVG5KMCBWNE","short_pith_number":"pith:5PNF5P4L","canonical_record":{"source":{"id":"1411.3156","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-12T12:28:21Z","cross_cats_sorted":[],"title_canon_sha256":"7287b592c640bef711b773f2ec2d71c7f7324c535f975dbfeb60dc34c7627332","abstract_canon_sha256":"108fb9d2fb0059e7dca3243f3be210f7cfe4a67ca7ff5979a8de1ee22a12322a"},"schema_version":"1.0"},"canonical_sha256":"ebda5ebf8bf9b0b4f9a6a9baa608366930eacb170ac186cd5bf6cabd62431732","source":{"kind":"arxiv","id":"1411.3156","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3156","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3156v1","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3156","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"pith_short_12","alias_value":"5PNF5P4L7GYL","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5PNF5P4L7GYLJ6NG","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5PNF5P4L","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:5PNF5P4L7GYLJ6NGVG5KMCBWNE","target":"record","payload":{"canonical_record":{"source":{"id":"1411.3156","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-12T12:28:21Z","cross_cats_sorted":[],"title_canon_sha256":"7287b592c640bef711b773f2ec2d71c7f7324c535f975dbfeb60dc34c7627332","abstract_canon_sha256":"108fb9d2fb0059e7dca3243f3be210f7cfe4a67ca7ff5979a8de1ee22a12322a"},"schema_version":"1.0"},"canonical_sha256":"ebda5ebf8bf9b0b4f9a6a9baa608366930eacb170ac186cd5bf6cabd62431732","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:45.637635Z","signature_b64":"S5tmilhxiJF7SQNCtJO9ywQWKlbIpVa8b5ZJuFhrNGSbx2FZOrfH6zXJP9IGb575Z9HUhnYu+KdhsZ5Oor4pDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebda5ebf8bf9b0b4f9a6a9baa608366930eacb170ac186cd5bf6cabd62431732","last_reissued_at":"2026-05-18T02:37:45.637109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:45.637109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.3156","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":"2026-05-18T02:37:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0BflgA4geRQZqWB6AqXbTLPQeP+Ih+9ykifzoQ44VnoXYawXcTiFRtTpOi+U1Py5b8VKb3Tpu24hvH3hFyASBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:10:19.240496Z"},"content_sha256":"1bb9443729b33a555ad8bc2813f5f1dd96ae6610ad6c246d8f56c1bd968e366b","schema_version":"1.0","event_id":"sha256:1bb9443729b33a555ad8bc2813f5f1dd96ae6610ad6c246d8f56c1bd968e366b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:5PNF5P4L7GYLJ6NGVG5KMCBWNE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sixty Years of Fractal Projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Jonathan Fraser, Kenneth Falconer, Xiong Jin","submitted_at":"2014-11-12T12:28:21Z","abstract_excerpt":"Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand's projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3156","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":""},"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":"2026-05-18T02:37:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pGD1/MsxZFXHQeWm/5JvURQqhf0x/OMIGNS1XNfPA3ko7ba2pLNOJExLwY05AXdGcLPBvMJ7BwQ8p+hpUiw8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:10:19.240831Z"},"content_sha256":"538658bba7eb87dd5534d90f54826476a74aeaebcb04e56839baf2c6ffe85440","schema_version":"1.0","event_id":"sha256:538658bba7eb87dd5534d90f54826476a74aeaebcb04e56839baf2c6ffe85440"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5PNF5P4L7GYLJ6NGVG5KMCBWNE/bundle.json","state_url":"https://pith.science/pith/5PNF5P4L7GYLJ6NGVG5KMCBWNE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5PNF5P4L7GYLJ6NGVG5KMCBWNE/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":"2026-06-20T06:10:19Z","links":{"resolver":"https://pith.science/pith/5PNF5P4L7GYLJ6NGVG5KMCBWNE","bundle":"https://pith.science/pith/5PNF5P4L7GYLJ6NGVG5KMCBWNE/bundle.json","state":"https://pith.science/pith/5PNF5P4L7GYLJ6NGVG5KMCBWNE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5PNF5P4L7GYLJ6NGVG5KMCBWNE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5PNF5P4L7GYLJ6NGVG5KMCBWNE","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":"108fb9d2fb0059e7dca3243f3be210f7cfe4a67ca7ff5979a8de1ee22a12322a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-12T12:28:21Z","title_canon_sha256":"7287b592c640bef711b773f2ec2d71c7f7324c535f975dbfeb60dc34c7627332"},"schema_version":"1.0","source":{"id":"1411.3156","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3156","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3156v1","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3156","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"pith_short_12","alias_value":"5PNF5P4L7GYL","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5PNF5P4L7GYLJ6NG","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5PNF5P4L","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:538658bba7eb87dd5534d90f54826476a74aeaebcb04e56839baf2c6ffe85440","target":"graph","created_at":"2026-05-18T02:37:45Z","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":"Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand's projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.","authors_text":"Jonathan Fraser, Kenneth Falconer, Xiong Jin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-12T12:28:21Z","title":"Sixty Years of Fractal Projections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3156","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":"sha256:1bb9443729b33a555ad8bc2813f5f1dd96ae6610ad6c246d8f56c1bd968e366b","target":"record","created_at":"2026-05-18T02:37:45Z","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":"108fb9d2fb0059e7dca3243f3be210f7cfe4a67ca7ff5979a8de1ee22a12322a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-12T12:28:21Z","title_canon_sha256":"7287b592c640bef711b773f2ec2d71c7f7324c535f975dbfeb60dc34c7627332"},"schema_version":"1.0","source":{"id":"1411.3156","kind":"arxiv","version":1}},"canonical_sha256":"ebda5ebf8bf9b0b4f9a6a9baa608366930eacb170ac186cd5bf6cabd62431732","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebda5ebf8bf9b0b4f9a6a9baa608366930eacb170ac186cd5bf6cabd62431732","first_computed_at":"2026-05-18T02:37:45.637109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:45.637109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S5tmilhxiJF7SQNCtJO9ywQWKlbIpVa8b5ZJuFhrNGSbx2FZOrfH6zXJP9IGb575Z9HUhnYu+KdhsZ5Oor4pDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:45.637635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.3156","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bb9443729b33a555ad8bc2813f5f1dd96ae6610ad6c246d8f56c1bd968e366b","sha256:538658bba7eb87dd5534d90f54826476a74aeaebcb04e56839baf2c6ffe85440"],"state_sha256":"b25cf9bb7e8bf7c52a0840ad2eaec2e234874e17f27bc5ea2bb8a8680abcdb17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OA2HtgwLdhJKWMOm7ZDoA66lX1GYMp/fAjm3qCXf1KwJqGCKGCuVYbBm9UCsQFMp/I9bc/0cEWmPcSP+uMt8Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:10:19.242700Z","bundle_sha256":"f04b6035bb2ddbd589445f2d2b8ba02647b30614d95cde2f87251efb27c3bd11"}}