{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:5ITTMNWL2NQXHODFQP5SK35LTB","short_pith_number":"pith:5ITTMNWL","canonical_record":{"source":{"id":"1009.0855","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-04T17:49:17Z","cross_cats_sorted":[],"title_canon_sha256":"14311409ef67863be0ef9e3f88f2c1fbb5e87beb11e169ad57a8da09ddaebab2","abstract_canon_sha256":"570f472e454c8b8cafc6a4e75840085231a586ffe0cbd3495e8efc8c022c0cc0"},"schema_version":"1.0"},"canonical_sha256":"ea273636cbd36173b86583fb256fab984be800a7bb1a0645ca6952eb6280d598","source":{"kind":"arxiv","id":"1009.0855","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0855","created_at":"2026-05-18T03:40:38Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0855v7","created_at":"2026-05-18T03:40:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0855","created_at":"2026-05-18T03:40:38Z"},{"alias_kind":"pith_short_12","alias_value":"5ITTMNWL2NQX","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5ITTMNWL2NQXHODF","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5ITTMNWL","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:5ITTMNWL2NQXHODFQP5SK35LTB","target":"record","payload":{"canonical_record":{"source":{"id":"1009.0855","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-04T17:49:17Z","cross_cats_sorted":[],"title_canon_sha256":"14311409ef67863be0ef9e3f88f2c1fbb5e87beb11e169ad57a8da09ddaebab2","abstract_canon_sha256":"570f472e454c8b8cafc6a4e75840085231a586ffe0cbd3495e8efc8c022c0cc0"},"schema_version":"1.0"},"canonical_sha256":"ea273636cbd36173b86583fb256fab984be800a7bb1a0645ca6952eb6280d598","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:38.868079Z","signature_b64":"wg89nGN6nxx6Q3O1W0/PHereBAhnDji5Ta8UTz71Opy4IrwG/tnX58Eh3nPwgr/QrW+noQw2MDz3+diaUVKQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea273636cbd36173b86583fb256fab984be800a7bb1a0645ca6952eb6280d598","last_reissued_at":"2026-05-18T03:40:38.867284Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:38.867284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.0855","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vrVHxrrM5liVEEdOB66wJcZlOYxs5AnbJdQTno9j/s2GZX+vuAnBgBupDeh0OmClC6lBmVOo/skUV7ODad1BCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:13:36.718496Z"},"content_sha256":"0d7bdc1cf75ac5e34ec2f063412838c640273cb718c8bf94f41e1c4338c0ab07","schema_version":"1.0","event_id":"sha256:0d7bdc1cf75ac5e34ec2f063412838c640273cb718c8bf94f41e1c4338c0ab07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:5ITTMNWL2NQXHODFQP5SK35LTB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Level Sets of the Takagi Function: Local Level Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jeffrey C. Lagarias, Zachary Maddock","submitted_at":"2010-09-04T17:49:17Z","abstract_excerpt":"The Takagi function \\tau : [0, 1] \\to [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. The level sets L(y) = {x : \\tau(x) = y} of the Takagi function \\tau(x) are studied by introducing a notion of local level set into which level sets are partitioned. Local level sets are simple to analyze, reducing questions to understanding the relation of level sets to local level sets, which is more complicated. It is known that for a \"generic\" full Lebesgue measure set of ordinates y, the level sets are finite sets. Here it is shown for a \"generic\" full Lebesgue measure se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0855","kind":"arxiv","version":7},"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":"2026-05-18T03:40:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oj7G/simrsXFrRvj16Mh+WZQT/iLaVoj18Pef/p1Ao+00vU+JBXKVdAZ0rsxqb07PPlY8JbzLyDO8lZnOklfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:13:36.718846Z"},"content_sha256":"03702e1bec9beb3caae8d7a92fb548ddb09e7a981c0c1e05bdf0ccfda42463aa","schema_version":"1.0","event_id":"sha256:03702e1bec9beb3caae8d7a92fb548ddb09e7a981c0c1e05bdf0ccfda42463aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5ITTMNWL2NQXHODFQP5SK35LTB/bundle.json","state_url":"https://pith.science/pith/5ITTMNWL2NQXHODFQP5SK35LTB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5ITTMNWL2NQXHODFQP5SK35LTB/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":"2026-05-27T08:13:36Z","links":{"resolver":"https://pith.science/pith/5ITTMNWL2NQXHODFQP5SK35LTB","bundle":"https://pith.science/pith/5ITTMNWL2NQXHODFQP5SK35LTB/bundle.json","state":"https://pith.science/pith/5ITTMNWL2NQXHODFQP5SK35LTB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5ITTMNWL2NQXHODFQP5SK35LTB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5ITTMNWL2NQXHODFQP5SK35LTB","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":"570f472e454c8b8cafc6a4e75840085231a586ffe0cbd3495e8efc8c022c0cc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-04T17:49:17Z","title_canon_sha256":"14311409ef67863be0ef9e3f88f2c1fbb5e87beb11e169ad57a8da09ddaebab2"},"schema_version":"1.0","source":{"id":"1009.0855","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0855","created_at":"2026-05-18T03:40:38Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0855v7","created_at":"2026-05-18T03:40:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0855","created_at":"2026-05-18T03:40:38Z"},{"alias_kind":"pith_short_12","alias_value":"5ITTMNWL2NQX","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5ITTMNWL2NQXHODF","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5ITTMNWL","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:03702e1bec9beb3caae8d7a92fb548ddb09e7a981c0c1e05bdf0ccfda42463aa","target":"graph","created_at":"2026-05-18T03:40:38Z","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":"The Takagi function \\tau : [0, 1] \\to [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. The level sets L(y) = {x : \\tau(x) = y} of the Takagi function \\tau(x) are studied by introducing a notion of local level set into which level sets are partitioned. Local level sets are simple to analyze, reducing questions to understanding the relation of level sets to local level sets, which is more complicated. It is known that for a \"generic\" full Lebesgue measure set of ordinates y, the level sets are finite sets. Here it is shown for a \"generic\" full Lebesgue measure se","authors_text":"Jeffrey C. Lagarias, Zachary Maddock","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-04T17:49:17Z","title":"Level Sets of the Takagi Function: Local Level Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0855","kind":"arxiv","version":7},"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":"sha256:0d7bdc1cf75ac5e34ec2f063412838c640273cb718c8bf94f41e1c4338c0ab07","target":"record","created_at":"2026-05-18T03:40:38Z","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":"570f472e454c8b8cafc6a4e75840085231a586ffe0cbd3495e8efc8c022c0cc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-04T17:49:17Z","title_canon_sha256":"14311409ef67863be0ef9e3f88f2c1fbb5e87beb11e169ad57a8da09ddaebab2"},"schema_version":"1.0","source":{"id":"1009.0855","kind":"arxiv","version":7}},"canonical_sha256":"ea273636cbd36173b86583fb256fab984be800a7bb1a0645ca6952eb6280d598","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea273636cbd36173b86583fb256fab984be800a7bb1a0645ca6952eb6280d598","first_computed_at":"2026-05-18T03:40:38.867284Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:38.867284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wg89nGN6nxx6Q3O1W0/PHereBAhnDji5Ta8UTz71Opy4IrwG/tnX58Eh3nPwgr/QrW+noQw2MDz3+diaUVKQAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:38.868079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0855","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d7bdc1cf75ac5e34ec2f063412838c640273cb718c8bf94f41e1c4338c0ab07","sha256:03702e1bec9beb3caae8d7a92fb548ddb09e7a981c0c1e05bdf0ccfda42463aa"],"state_sha256":"ca79d57f5cf55ccdb0938f75b5f1256b5ff47b8948529b1dedfc2c75c380e63a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"11Z0OBLXE+QqOC+9tMYsXD7Fu3Wf/xQ0Hw6hiVvNFlBdstDnqmDQm2HsvpeyUuSSknRfausV5Qh9JpOdyxisDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:13:36.721392Z","bundle_sha256":"d17bb2b525a4b2ae869b78d87da3d5749f3b84079c910e472741b32eb470eda0"}}