{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:MTFL5E7CZM6DD5KJGODX6EELFK","short_pith_number":"pith:MTFL5E7C","canonical_record":{"source":{"id":"2404.16315","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-04-25T03:45:05Z","cross_cats_sorted":[],"title_canon_sha256":"cd47d4c67004307e05de3d01f257b6f474fbd7fc2b2330a7729691fea0154b74","abstract_canon_sha256":"c3768e58976cdde6b1472e231cec7f99fde854b5f61ac5c70357b968b73dd558"},"schema_version":"1.0"},"canonical_sha256":"64cabe93e2cb3c31f54933877f108b2a91ce8f92e61a6a25d9b218bb872ab071","source":{"kind":"arxiv","id":"2404.16315","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.16315","created_at":"2026-07-05T10:27:09Z"},{"alias_kind":"arxiv_version","alias_value":"2404.16315v3","created_at":"2026-07-05T10:27:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.16315","created_at":"2026-07-05T10:27:09Z"},{"alias_kind":"pith_short_12","alias_value":"MTFL5E7CZM6D","created_at":"2026-07-05T10:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"MTFL5E7CZM6DD5KJ","created_at":"2026-07-05T10:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"MTFL5E7C","created_at":"2026-07-05T10:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:MTFL5E7CZM6DD5KJGODX6EELFK","target":"record","payload":{"canonical_record":{"source":{"id":"2404.16315","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-04-25T03:45:05Z","cross_cats_sorted":[],"title_canon_sha256":"cd47d4c67004307e05de3d01f257b6f474fbd7fc2b2330a7729691fea0154b74","abstract_canon_sha256":"c3768e58976cdde6b1472e231cec7f99fde854b5f61ac5c70357b968b73dd558"},"schema_version":"1.0"},"canonical_sha256":"64cabe93e2cb3c31f54933877f108b2a91ce8f92e61a6a25d9b218bb872ab071","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:27:09.530801Z","signature_b64":"vPZLGeLxzFW+QWKvWNtGILJapSGaR/UaQ7Qqr4Vkq2Y8T8LvZFohEEASkvuHJtZyYdowBr/0qS41oAC76nVSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64cabe93e2cb3c31f54933877f108b2a91ce8f92e61a6a25d9b218bb872ab071","last_reissued_at":"2026-07-05T10:27:09.529911Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:27:09.529911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.16315","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:27:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cAyt3k0BA8PGiAVLriqbt+2RJXDjx1v1wrk2WQAocQaZ5dIL2qu9bMoKoB0w+FxmF9WJSTkHuRqEtiGjyIeuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T20:45:48.732766Z"},"content_sha256":"6630fb478a0a393d26f1eb0316c9285b7809c3693b5080746f65327c9e065d63","schema_version":"1.0","event_id":"sha256:6630fb478a0a393d26f1eb0316c9285b7809c3693b5080746f65327c9e065d63"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:MTFL5E7CZM6DD5KJGODX6EELFK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds on the dimension of lineal extensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jacob B. Fiedler, Ryan E. G. Bushling","submitted_at":"2024-04-25T03:45:05Z","abstract_excerpt":"Let $E \\subseteq \\mathbb{R}^n$ be a union of line segments and $F \\subseteq \\mathbb{R}^n$ the set obtained from $E$ by extending each line segment in $E$ to a full line. Keleti's line segment extension conjecture posits that the Hausdorff dimension of $F$ should equal that of $E$. Working in $\\mathbb{R}^2$, we use effective methods to prove a strong packing dimension variant of this conjecture, from which the generalized Kakeya conjecture for packing dimension immediately follows. This is followed by several doubling estimates in higher dimensions and connections to related problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.16315","kind":"arxiv","version":3},"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/2404.16315/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":"2026-07-05T10:27:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MClGaOaXMuDWKBFxISa/GVR55IUaL8pJ3rcpc/755I6+I2Rze5xiRq4a9WwxNxd2B4b0oUHAuDhfioEaPciECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T20:45:48.733385Z"},"content_sha256":"33e501d6b3d7ab0c8fb656127e56184a1b44102ff5c6e245c1afc0303cb9422c","schema_version":"1.0","event_id":"sha256:33e501d6b3d7ab0c8fb656127e56184a1b44102ff5c6e245c1afc0303cb9422c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MTFL5E7CZM6DD5KJGODX6EELFK/bundle.json","state_url":"https://pith.science/pith/MTFL5E7CZM6DD5KJGODX6EELFK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MTFL5E7CZM6DD5KJGODX6EELFK/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":"2026-08-18T20:45:48Z","links":{"resolver":"https://pith.science/pith/MTFL5E7CZM6DD5KJGODX6EELFK","bundle":"https://pith.science/pith/MTFL5E7CZM6DD5KJGODX6EELFK/bundle.json","state":"https://pith.science/pith/MTFL5E7CZM6DD5KJGODX6EELFK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MTFL5E7CZM6DD5KJGODX6EELFK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:MTFL5E7CZM6DD5KJGODX6EELFK","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":"c3768e58976cdde6b1472e231cec7f99fde854b5f61ac5c70357b968b73dd558","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-04-25T03:45:05Z","title_canon_sha256":"cd47d4c67004307e05de3d01f257b6f474fbd7fc2b2330a7729691fea0154b74"},"schema_version":"1.0","source":{"id":"2404.16315","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.16315","created_at":"2026-07-05T10:27:09Z"},{"alias_kind":"arxiv_version","alias_value":"2404.16315v3","created_at":"2026-07-05T10:27:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.16315","created_at":"2026-07-05T10:27:09Z"},{"alias_kind":"pith_short_12","alias_value":"MTFL5E7CZM6D","created_at":"2026-07-05T10:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"MTFL5E7CZM6DD5KJ","created_at":"2026-07-05T10:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"MTFL5E7C","created_at":"2026-07-05T10:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:33e501d6b3d7ab0c8fb656127e56184a1b44102ff5c6e245c1afc0303cb9422c","target":"graph","created_at":"2026-07-05T10:27:09Z","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/2404.16315/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $E \\subseteq \\mathbb{R}^n$ be a union of line segments and $F \\subseteq \\mathbb{R}^n$ the set obtained from $E$ by extending each line segment in $E$ to a full line. Keleti's line segment extension conjecture posits that the Hausdorff dimension of $F$ should equal that of $E$. Working in $\\mathbb{R}^2$, we use effective methods to prove a strong packing dimension variant of this conjecture, from which the generalized Kakeya conjecture for packing dimension immediately follows. This is followed by several doubling estimates in higher dimensions and connections to related problems.","authors_text":"Jacob B. Fiedler, Ryan E. G. Bushling","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-04-25T03:45:05Z","title":"Bounds on the dimension of lineal extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.16315","kind":"arxiv","version":3},"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":"sha256:6630fb478a0a393d26f1eb0316c9285b7809c3693b5080746f65327c9e065d63","target":"record","created_at":"2026-07-05T10:27:09Z","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":"c3768e58976cdde6b1472e231cec7f99fde854b5f61ac5c70357b968b73dd558","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-04-25T03:45:05Z","title_canon_sha256":"cd47d4c67004307e05de3d01f257b6f474fbd7fc2b2330a7729691fea0154b74"},"schema_version":"1.0","source":{"id":"2404.16315","kind":"arxiv","version":3}},"canonical_sha256":"64cabe93e2cb3c31f54933877f108b2a91ce8f92e61a6a25d9b218bb872ab071","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64cabe93e2cb3c31f54933877f108b2a91ce8f92e61a6a25d9b218bb872ab071","first_computed_at":"2026-07-05T10:27:09.529911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:27:09.529911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vPZLGeLxzFW+QWKvWNtGILJapSGaR/UaQ7Qqr4Vkq2Y8T8LvZFohEEASkvuHJtZyYdowBr/0qS41oAC76nVSBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:27:09.530801Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.16315","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6630fb478a0a393d26f1eb0316c9285b7809c3693b5080746f65327c9e065d63","sha256:33e501d6b3d7ab0c8fb656127e56184a1b44102ff5c6e245c1afc0303cb9422c"],"state_sha256":"76b7b29614d5be59c1f5cdbae21bedcc0270ce4906a8724c77411051a3850e08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AlKW6GcwOaGd2NMp6p/E3hD0b8aKt4ux2ln4g4yDy0V9OBWYcD/PtIhbi6SDmJTZ1IIDD7Ck4vRj8/plaT3HCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T20:45:48.738263Z","bundle_sha256":"86f4e5836d8ad6b3f38a575927fddcb657e773e46fa7934fea10d40746184d2a"}}