{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:F6QB3JGD4RDL6VZSYJTW3XNOYG","short_pith_number":"pith:F6QB3JGD","canonical_record":{"source":{"id":"2305.06937","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-05-11T16:14:38Z","cross_cats_sorted":[],"title_canon_sha256":"43da8551e9865c3cc2ab2b2b29434fbb6cf177e2005c46ba8066612194f8d559","abstract_canon_sha256":"9ecd3704255708cb7c641fe4fabffbe478e7eda3f0295c1c4a7104836a93aa1b"},"schema_version":"1.0"},"canonical_sha256":"2fa01da4c3e446bf5732c2676dddaec1b23cc17c077b22d1cc5d8eaa4b368c00","source":{"kind":"arxiv","id":"2305.06937","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.06937","created_at":"2026-07-05T09:29:48Z"},{"alias_kind":"arxiv_version","alias_value":"2305.06937v3","created_at":"2026-07-05T09:29:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.06937","created_at":"2026-07-05T09:29:48Z"},{"alias_kind":"pith_short_12","alias_value":"F6QB3JGD4RDL","created_at":"2026-07-05T09:29:48Z"},{"alias_kind":"pith_short_16","alias_value":"F6QB3JGD4RDL6VZS","created_at":"2026-07-05T09:29:48Z"},{"alias_kind":"pith_short_8","alias_value":"F6QB3JGD","created_at":"2026-07-05T09:29:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:F6QB3JGD4RDL6VZSYJTW3XNOYG","target":"record","payload":{"canonical_record":{"source":{"id":"2305.06937","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-05-11T16:14:38Z","cross_cats_sorted":[],"title_canon_sha256":"43da8551e9865c3cc2ab2b2b29434fbb6cf177e2005c46ba8066612194f8d559","abstract_canon_sha256":"9ecd3704255708cb7c641fe4fabffbe478e7eda3f0295c1c4a7104836a93aa1b"},"schema_version":"1.0"},"canonical_sha256":"2fa01da4c3e446bf5732c2676dddaec1b23cc17c077b22d1cc5d8eaa4b368c00","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:29:48.408670Z","signature_b64":"lNEASMwZP20HbQHUVmeO+AWXvTKZ7Mo49p3AoeA0p9SIWjn/gLQ8QPRjNPCqBo3Es81yTy3MEGewd0uxfDCUAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fa01da4c3e446bf5732c2676dddaec1b23cc17c077b22d1cc5d8eaa4b368c00","last_reissued_at":"2026-07-05T09:29:48.408259Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:29:48.408259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2305.06937","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":"2026-07-05T09:29:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U+kToGSSpAXuII54NNgNvEi6C0ih1vX2Z5FWEdaQ/ABAFXuVHgT1INIZGDAWK3anQ/24SO25QYffA+jwlKq5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T14:12:54.139893Z"},"content_sha256":"d43235b7f26278d7c70a769418e3eb4afa199c05021357c92e641046f0a677ed","schema_version":"1.0","event_id":"sha256:d43235b7f26278d7c70a769418e3eb4afa199c05021357c92e641046f0a677ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:F6QB3JGD4RDL6VZSYJTW3XNOYG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distance sets bounds for polyhedral norms via effective dimension","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bobby Wilson, Iqra Altaf, Ryan Bushling","submitted_at":"2023-05-11T16:14:38Z","abstract_excerpt":"We prove that, for every norm on $\\mathbb{R}^d$ and every $E \\subseteq \\mathbb{R}^d$, the Hausdorff dimension of the distance set of $E$ with respect to that norm is at least $\\dim_{\\mathrm{H}} E - (d-1)$. An explicit construction follows, demonstrating that this bound is sharp for every polyhedral norm on $\\mathbb{R}^d$. The techniques of algorithmic complexity theory underlie both the computations and the construction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.06937","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/2305.06937/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":"2026-07-05T09:29:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ENEcjbkACa7D3RHn9pwyTa/XiF1PqX9RP8F4URKp03Eie4dS2h7t/7X2fb/vBhjBuTX8LHR+zasqgw5+RDdqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T14:12:54.140419Z"},"content_sha256":"461a90f1ed57dfad7ac4451f27a26685fa66869a654b834af4348261598bd374","schema_version":"1.0","event_id":"sha256:461a90f1ed57dfad7ac4451f27a26685fa66869a654b834af4348261598bd374"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F6QB3JGD4RDL6VZSYJTW3XNOYG/bundle.json","state_url":"https://pith.science/pith/F6QB3JGD4RDL6VZSYJTW3XNOYG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F6QB3JGD4RDL6VZSYJTW3XNOYG/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":"2026-08-09T14:12:54Z","links":{"resolver":"https://pith.science/pith/F6QB3JGD4RDL6VZSYJTW3XNOYG","bundle":"https://pith.science/pith/F6QB3JGD4RDL6VZSYJTW3XNOYG/bundle.json","state":"https://pith.science/pith/F6QB3JGD4RDL6VZSYJTW3XNOYG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F6QB3JGD4RDL6VZSYJTW3XNOYG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:F6QB3JGD4RDL6VZSYJTW3XNOYG","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":"9ecd3704255708cb7c641fe4fabffbe478e7eda3f0295c1c4a7104836a93aa1b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-05-11T16:14:38Z","title_canon_sha256":"43da8551e9865c3cc2ab2b2b29434fbb6cf177e2005c46ba8066612194f8d559"},"schema_version":"1.0","source":{"id":"2305.06937","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.06937","created_at":"2026-07-05T09:29:48Z"},{"alias_kind":"arxiv_version","alias_value":"2305.06937v3","created_at":"2026-07-05T09:29:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.06937","created_at":"2026-07-05T09:29:48Z"},{"alias_kind":"pith_short_12","alias_value":"F6QB3JGD4RDL","created_at":"2026-07-05T09:29:48Z"},{"alias_kind":"pith_short_16","alias_value":"F6QB3JGD4RDL6VZS","created_at":"2026-07-05T09:29:48Z"},{"alias_kind":"pith_short_8","alias_value":"F6QB3JGD","created_at":"2026-07-05T09:29:48Z"}],"graph_snapshots":[{"event_id":"sha256:461a90f1ed57dfad7ac4451f27a26685fa66869a654b834af4348261598bd374","target":"graph","created_at":"2026-07-05T09:29:48Z","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/2305.06937/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that, for every norm on $\\mathbb{R}^d$ and every $E \\subseteq \\mathbb{R}^d$, the Hausdorff dimension of the distance set of $E$ with respect to that norm is at least $\\dim_{\\mathrm{H}} E - (d-1)$. An explicit construction follows, demonstrating that this bound is sharp for every polyhedral norm on $\\mathbb{R}^d$. The techniques of algorithmic complexity theory underlie both the computations and the construction.","authors_text":"Bobby Wilson, Iqra Altaf, Ryan Bushling","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-05-11T16:14:38Z","title":"Distance sets bounds for polyhedral norms via effective dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.06937","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:d43235b7f26278d7c70a769418e3eb4afa199c05021357c92e641046f0a677ed","target":"record","created_at":"2026-07-05T09:29:48Z","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":"9ecd3704255708cb7c641fe4fabffbe478e7eda3f0295c1c4a7104836a93aa1b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-05-11T16:14:38Z","title_canon_sha256":"43da8551e9865c3cc2ab2b2b29434fbb6cf177e2005c46ba8066612194f8d559"},"schema_version":"1.0","source":{"id":"2305.06937","kind":"arxiv","version":3}},"canonical_sha256":"2fa01da4c3e446bf5732c2676dddaec1b23cc17c077b22d1cc5d8eaa4b368c00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fa01da4c3e446bf5732c2676dddaec1b23cc17c077b22d1cc5d8eaa4b368c00","first_computed_at":"2026-07-05T09:29:48.408259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:29:48.408259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lNEASMwZP20HbQHUVmeO+AWXvTKZ7Mo49p3AoeA0p9SIWjn/gLQ8QPRjNPCqBo3Es81yTy3MEGewd0uxfDCUAA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:29:48.408670Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.06937","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d43235b7f26278d7c70a769418e3eb4afa199c05021357c92e641046f0a677ed","sha256:461a90f1ed57dfad7ac4451f27a26685fa66869a654b834af4348261598bd374"],"state_sha256":"0cc900c96f9b8175941d004c81c2e65a79ab583e41df94815a836439778fba29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"we2Gt4/Q/ig9Q/3zbZqJ+lq8JvO+ksj8wLjcaoLx1uJqCN1MC8wpYQznrGE42Z+QooNLtNghTA+ldEgYODVPDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T14:12:54.143731Z","bundle_sha256":"22694c3938611ee4a846e5644bbaa54ac5dfa79632eab7b6a10a698a00bba135"}}