{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:U6D2QQMFO2RXTHLG5KG5Z23WDE","short_pith_number":"pith:U6D2QQMF","canonical_record":{"source":{"id":"2506.05541","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-06-05T19:44:35Z","cross_cats_sorted":[],"title_canon_sha256":"8f33bb5eddc7a0b7227fcc7a13d1d82341394af1929ce1e12cafd7ce54a67132","abstract_canon_sha256":"c91e08483aeb54959da42f131cb952c5e49ca9119a00aebea7fde79347b35f25"},"schema_version":"1.0"},"canonical_sha256":"a787a8418576a3799d66ea8ddceb76193d09fe1eda74ca0ef91753e79037e3c1","source":{"kind":"arxiv","id":"2506.05541","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.05541","created_at":"2026-07-05T11:26:52Z"},{"alias_kind":"arxiv_version","alias_value":"2506.05541v2","created_at":"2026-07-05T11:26:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05541","created_at":"2026-07-05T11:26:52Z"},{"alias_kind":"pith_short_12","alias_value":"U6D2QQMFO2RX","created_at":"2026-07-05T11:26:52Z"},{"alias_kind":"pith_short_16","alias_value":"U6D2QQMFO2RXTHLG","created_at":"2026-07-05T11:26:52Z"},{"alias_kind":"pith_short_8","alias_value":"U6D2QQMF","created_at":"2026-07-05T11:26:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:U6D2QQMFO2RXTHLG5KG5Z23WDE","target":"record","payload":{"canonical_record":{"source":{"id":"2506.05541","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-06-05T19:44:35Z","cross_cats_sorted":[],"title_canon_sha256":"8f33bb5eddc7a0b7227fcc7a13d1d82341394af1929ce1e12cafd7ce54a67132","abstract_canon_sha256":"c91e08483aeb54959da42f131cb952c5e49ca9119a00aebea7fde79347b35f25"},"schema_version":"1.0"},"canonical_sha256":"a787a8418576a3799d66ea8ddceb76193d09fe1eda74ca0ef91753e79037e3c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:26:52.324140Z","signature_b64":"EBzzsedv05AvZQsa/9d6UwQ3dlI7AeNvFPLCUd+8EAI8OLuuqsUsM9D6DldUGbAIy8XgS11m+tgyH/xDhEBuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a787a8418576a3799d66ea8ddceb76193d09fe1eda74ca0ef91753e79037e3c1","last_reissued_at":"2026-07-05T11:26:52.323612Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:26:52.323612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.05541","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":"2026-07-05T11:26:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KlrC6Lld2gkUuhnnAtwdVnzKOK4VBBb00FInuK8HL3GU9cW1EkFf1KWWuqkmX8GxPKrSNH+Ml199vYDZd3KWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:52:21.705017Z"},"content_sha256":"2778db676d5705af77bd33869b58cc98dd1832ae568f96395d5c3555328d4435","schema_version":"1.0","event_id":"sha256:2778db676d5705af77bd33869b58cc98dd1832ae568f96395d5c3555328d4435"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:U6D2QQMFO2RXTHLG5KG5Z23WDE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The coordinate functions of the Heighway dragon curve","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Danilo Antonio Caprio","submitted_at":"2025-06-05T19:44:35Z","abstract_excerpt":"In this work, we study properties of the coordinate functions $x_\\theta$ and $y_\\theta$ of the dragon curve associated with the angle $\\frac{\\pi}{3} < \\theta < \\frac{5\\pi}{3}$, and we prove that the box-counting dimension of its graph is equal to $1 - \\frac{\\log \\cos\\alpha}{\\log 2}$, where $\\alpha = \\frac{\\pi - \\theta}{2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05541","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.05541/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":"2026-07-05T11:26:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hWRmg4GEnb3QYYKc/J8xSdkN0uE8ypZi9v04078CtUkeyIPnZWgV64KdneZ5AxorKC7zWaAai0kX5dXp7mmzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:52:21.705494Z"},"content_sha256":"d9dde35b0ba3ccaafef6a91b45e84fa63ea37a65613bf03c5f43bc9090193376","schema_version":"1.0","event_id":"sha256:d9dde35b0ba3ccaafef6a91b45e84fa63ea37a65613bf03c5f43bc9090193376"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U6D2QQMFO2RXTHLG5KG5Z23WDE/bundle.json","state_url":"https://pith.science/pith/U6D2QQMFO2RXTHLG5KG5Z23WDE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U6D2QQMFO2RXTHLG5KG5Z23WDE/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":"2026-08-08T11:52:21Z","links":{"resolver":"https://pith.science/pith/U6D2QQMFO2RXTHLG5KG5Z23WDE","bundle":"https://pith.science/pith/U6D2QQMFO2RXTHLG5KG5Z23WDE/bundle.json","state":"https://pith.science/pith/U6D2QQMFO2RXTHLG5KG5Z23WDE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U6D2QQMFO2RXTHLG5KG5Z23WDE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:U6D2QQMFO2RXTHLG5KG5Z23WDE","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":"c91e08483aeb54959da42f131cb952c5e49ca9119a00aebea7fde79347b35f25","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-06-05T19:44:35Z","title_canon_sha256":"8f33bb5eddc7a0b7227fcc7a13d1d82341394af1929ce1e12cafd7ce54a67132"},"schema_version":"1.0","source":{"id":"2506.05541","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.05541","created_at":"2026-07-05T11:26:52Z"},{"alias_kind":"arxiv_version","alias_value":"2506.05541v2","created_at":"2026-07-05T11:26:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05541","created_at":"2026-07-05T11:26:52Z"},{"alias_kind":"pith_short_12","alias_value":"U6D2QQMFO2RX","created_at":"2026-07-05T11:26:52Z"},{"alias_kind":"pith_short_16","alias_value":"U6D2QQMFO2RXTHLG","created_at":"2026-07-05T11:26:52Z"},{"alias_kind":"pith_short_8","alias_value":"U6D2QQMF","created_at":"2026-07-05T11:26:52Z"}],"graph_snapshots":[{"event_id":"sha256:d9dde35b0ba3ccaafef6a91b45e84fa63ea37a65613bf03c5f43bc9090193376","target":"graph","created_at":"2026-07-05T11:26:52Z","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/2506.05541/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we study properties of the coordinate functions $x_\\theta$ and $y_\\theta$ of the dragon curve associated with the angle $\\frac{\\pi}{3} < \\theta < \\frac{5\\pi}{3}$, and we prove that the box-counting dimension of its graph is equal to $1 - \\frac{\\log \\cos\\alpha}{\\log 2}$, where $\\alpha = \\frac{\\pi - \\theta}{2}$.","authors_text":"Danilo Antonio Caprio","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-06-05T19:44:35Z","title":"The coordinate functions of the Heighway dragon curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05541","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":"sha256:2778db676d5705af77bd33869b58cc98dd1832ae568f96395d5c3555328d4435","target":"record","created_at":"2026-07-05T11:26:52Z","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":"c91e08483aeb54959da42f131cb952c5e49ca9119a00aebea7fde79347b35f25","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-06-05T19:44:35Z","title_canon_sha256":"8f33bb5eddc7a0b7227fcc7a13d1d82341394af1929ce1e12cafd7ce54a67132"},"schema_version":"1.0","source":{"id":"2506.05541","kind":"arxiv","version":2}},"canonical_sha256":"a787a8418576a3799d66ea8ddceb76193d09fe1eda74ca0ef91753e79037e3c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a787a8418576a3799d66ea8ddceb76193d09fe1eda74ca0ef91753e79037e3c1","first_computed_at":"2026-07-05T11:26:52.323612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:26:52.323612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EBzzsedv05AvZQsa/9d6UwQ3dlI7AeNvFPLCUd+8EAI8OLuuqsUsM9D6DldUGbAIy8XgS11m+tgyH/xDhEBuDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:26:52.324140Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.05541","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2778db676d5705af77bd33869b58cc98dd1832ae568f96395d5c3555328d4435","sha256:d9dde35b0ba3ccaafef6a91b45e84fa63ea37a65613bf03c5f43bc9090193376"],"state_sha256":"0e1351887fd2900a4f5d81695431540deab111f632c431048148dd944d8dcfc2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hraTE7QuNy4qVFqUn049dG9bNbRt7zjydaY74RfXRGGz1y527sHwWQ3yhH8f5D8unBCfUYXsisU1g9hAMr/0Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T11:52:21.708931Z","bundle_sha256":"a307cf0727c3d3dfe3621eb9c618db7467f5ed75976dac2ef39224ffe836e04e"}}