{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YPVZ63UR7IS74D7GRIDPJ42NAK","short_pith_number":"pith:YPVZ63UR","canonical_record":{"source":{"id":"1211.4541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-19T19:31:53Z","cross_cats_sorted":[],"title_canon_sha256":"5b910c5391f5a3c4a13cf0de5e6fd1c79daf74c0089b252b044ed1240b6cd78c","abstract_canon_sha256":"4b7f846aa2fae1d7bed6bfd7a5838cafef6ddfd88ec33632736aa105840858a3"},"schema_version":"1.0"},"canonical_sha256":"c3eb9f6e91fa25fe0fe68a06f4f34d02b3eb158c3f3f3157ab8733c7bdd87d99","source":{"kind":"arxiv","id":"1211.4541","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4541","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4541v1","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4541","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"pith_short_12","alias_value":"YPVZ63UR7IS7","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YPVZ63UR7IS74D7G","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YPVZ63UR","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YPVZ63UR7IS74D7GRIDPJ42NAK","target":"record","payload":{"canonical_record":{"source":{"id":"1211.4541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-19T19:31:53Z","cross_cats_sorted":[],"title_canon_sha256":"5b910c5391f5a3c4a13cf0de5e6fd1c79daf74c0089b252b044ed1240b6cd78c","abstract_canon_sha256":"4b7f846aa2fae1d7bed6bfd7a5838cafef6ddfd88ec33632736aa105840858a3"},"schema_version":"1.0"},"canonical_sha256":"c3eb9f6e91fa25fe0fe68a06f4f34d02b3eb158c3f3f3157ab8733c7bdd87d99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:26.595028Z","signature_b64":"45K84seCFcKkwDGu6gn+w7gyjoY4nkR/xDs1pTmne7baLkKvr7ud9Zx/95IpbZZUKYcreaam3JzgGTcHQvGfBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3eb9f6e91fa25fe0fe68a06f4f34d02b3eb158c3f3f3157ab8733c7bdd87d99","last_reissued_at":"2026-05-18T03:40:26.594486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:26.594486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.4541","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":"2026-05-18T03:40:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EZBF5BCqWw6efCA4snaXVovcNiMhFNYcAMYxL/0v7uswtuv9OjaEpWFnGWcbLJOdPaU9rjDZ+SogMivnERjsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:51:46.737101Z"},"content_sha256":"ff57d46927835456d87d4f07421f0aefc814e0f6234fc51f2f7162f6c6a10fc2","schema_version":"1.0","event_id":"sha256:ff57d46927835456d87d4f07421f0aefc814e0f6234fc51f2f7162f6c6a10fc2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YPVZ63UR7IS74D7GRIDPJ42NAK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the derivative of the \\alpha-Farey-Minkowski function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sara Munday","submitted_at":"2012-11-19T19:31:53Z","abstract_excerpt":"In this paper we study the family of $\\alpha$-Farey-Minkowski functions $\\theta_\\alpha$, for an arbitrary countable partition $\\alpha$ of the unit interval with atoms which accumulate only at the origin, which are the conjugating homeomorphisms between each of the $\\alpha$-Farey systems and the tent map. We first show that each function $\\theta_\\alpha$ is singular with respect to the Lebesgue measure and then demonstrate that the unit interval can be written as the disjoint union of the following three sets: $\\Theta_0:={x\\in\\U:\\theta_\\alpha'(x)=0}, \\Theta_\\infty:={x\\in\\U:\\theta_\\alpha'(x)=\\inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4541","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":"2026-05-18T03:40:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vKB2hUXVBtJTCIW3Jsp1lpWnTekDtaQkjpErK0NdHtvjP07kAOKE0quPd+W1hASZxkq1bsUCE3p2nsZX2ChiCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:51:46.737476Z"},"content_sha256":"b0bd72e95703caae8d502dcfa5a1d2c15f51776a0ed3e63a3870211038b8d54d","schema_version":"1.0","event_id":"sha256:b0bd72e95703caae8d502dcfa5a1d2c15f51776a0ed3e63a3870211038b8d54d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YPVZ63UR7IS74D7GRIDPJ42NAK/bundle.json","state_url":"https://pith.science/pith/YPVZ63UR7IS74D7GRIDPJ42NAK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YPVZ63UR7IS74D7GRIDPJ42NAK/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":"2026-06-23T13:51:46Z","links":{"resolver":"https://pith.science/pith/YPVZ63UR7IS74D7GRIDPJ42NAK","bundle":"https://pith.science/pith/YPVZ63UR7IS74D7GRIDPJ42NAK/bundle.json","state":"https://pith.science/pith/YPVZ63UR7IS74D7GRIDPJ42NAK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YPVZ63UR7IS74D7GRIDPJ42NAK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YPVZ63UR7IS74D7GRIDPJ42NAK","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":"4b7f846aa2fae1d7bed6bfd7a5838cafef6ddfd88ec33632736aa105840858a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-19T19:31:53Z","title_canon_sha256":"5b910c5391f5a3c4a13cf0de5e6fd1c79daf74c0089b252b044ed1240b6cd78c"},"schema_version":"1.0","source":{"id":"1211.4541","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4541","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4541v1","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4541","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"pith_short_12","alias_value":"YPVZ63UR7IS7","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YPVZ63UR7IS74D7G","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YPVZ63UR","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:b0bd72e95703caae8d502dcfa5a1d2c15f51776a0ed3e63a3870211038b8d54d","target":"graph","created_at":"2026-05-18T03:40:26Z","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":"In this paper we study the family of $\\alpha$-Farey-Minkowski functions $\\theta_\\alpha$, for an arbitrary countable partition $\\alpha$ of the unit interval with atoms which accumulate only at the origin, which are the conjugating homeomorphisms between each of the $\\alpha$-Farey systems and the tent map. We first show that each function $\\theta_\\alpha$ is singular with respect to the Lebesgue measure and then demonstrate that the unit interval can be written as the disjoint union of the following three sets: $\\Theta_0:={x\\in\\U:\\theta_\\alpha'(x)=0}, \\Theta_\\infty:={x\\in\\U:\\theta_\\alpha'(x)=\\inf","authors_text":"Sara Munday","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-19T19:31:53Z","title":"On the derivative of the \\alpha-Farey-Minkowski function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4541","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:ff57d46927835456d87d4f07421f0aefc814e0f6234fc51f2f7162f6c6a10fc2","target":"record","created_at":"2026-05-18T03:40:26Z","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":"4b7f846aa2fae1d7bed6bfd7a5838cafef6ddfd88ec33632736aa105840858a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-19T19:31:53Z","title_canon_sha256":"5b910c5391f5a3c4a13cf0de5e6fd1c79daf74c0089b252b044ed1240b6cd78c"},"schema_version":"1.0","source":{"id":"1211.4541","kind":"arxiv","version":1}},"canonical_sha256":"c3eb9f6e91fa25fe0fe68a06f4f34d02b3eb158c3f3f3157ab8733c7bdd87d99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3eb9f6e91fa25fe0fe68a06f4f34d02b3eb158c3f3f3157ab8733c7bdd87d99","first_computed_at":"2026-05-18T03:40:26.594486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:26.594486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"45K84seCFcKkwDGu6gn+w7gyjoY4nkR/xDs1pTmne7baLkKvr7ud9Zx/95IpbZZUKYcreaam3JzgGTcHQvGfBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:26.595028Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.4541","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff57d46927835456d87d4f07421f0aefc814e0f6234fc51f2f7162f6c6a10fc2","sha256:b0bd72e95703caae8d502dcfa5a1d2c15f51776a0ed3e63a3870211038b8d54d"],"state_sha256":"0d6b725db24de0556dc20af347548c0009b34cd7fff6e04d0c8d7e5b945672f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y90YwH7VOhQPCT7iWvnuHGhrO6ws+vktxWUUnuJrggJO6+/hT9OjtRUTfIJ6wdU5OYT45rbLeVj/SoP6/OHVDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T13:51:46.739392Z","bundle_sha256":"2b8ba077d5594a1de23da311d60b7e31fd2aedefe83b189a83ee21fb7283ba5c"}}