{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:PG7NCPVLR5UQP5POGUQ3I3YIFI","short_pith_number":"pith:PG7NCPVL","canonical_record":{"source":{"id":"cond-mat/9610177","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.mes-hall","submitted_at":"1996-10-24T13:34:46Z","cross_cats_sorted":[],"title_canon_sha256":"2d63c80c1e2111a29e8ed7cff37409253658310d828e4e0e414e12572f548d3a","abstract_canon_sha256":"b6ec50312857f2ed583ae6ac066b65de37e4e44d56cb5662ad7b1240470419d4"},"schema_version":"1.0"},"canonical_sha256":"79bed13eab8f6907f5ee3521b46f082a0e3c918efe6c7d1bea10cc7c9349dbdd","source":{"kind":"arxiv","id":"cond-mat/9610177","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9610177","created_at":"2026-05-18T01:07:09Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9610177v1","created_at":"2026-05-18T01:07:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9610177","created_at":"2026-05-18T01:07:09Z"},{"alias_kind":"pith_short_12","alias_value":"PG7NCPVLR5UQ","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"PG7NCPVLR5UQP5PO","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"PG7NCPVL","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:PG7NCPVLR5UQP5POGUQ3I3YIFI","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/9610177","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.mes-hall","submitted_at":"1996-10-24T13:34:46Z","cross_cats_sorted":[],"title_canon_sha256":"2d63c80c1e2111a29e8ed7cff37409253658310d828e4e0e414e12572f548d3a","abstract_canon_sha256":"b6ec50312857f2ed583ae6ac066b65de37e4e44d56cb5662ad7b1240470419d4"},"schema_version":"1.0"},"canonical_sha256":"79bed13eab8f6907f5ee3521b46f082a0e3c918efe6c7d1bea10cc7c9349dbdd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:09.187875Z","signature_b64":"wVsOjTvWqXKgCseT9ERA7wY6NzNXx5+/RdVE179HI0Y9/CiAfyuFxs1n7JzP8UE2itd5rQglZp7phSAJk7RaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79bed13eab8f6907f5ee3521b46f082a0e3c918efe6c7d1bea10cc7c9349dbdd","last_reissued_at":"2026-05-18T01:07:09.187534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:09.187534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/9610177","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":"2026-05-18T01:07:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bw2r5gIMiEa12LQ4t6LAc7sOiaPai8B9RVVhuYhHQGoXbR1RYtYYTT62GG6a7Dt0K7GgOOyAmq42OYLTG/UuAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:26:19.566463Z"},"content_sha256":"71e6c421b6b9c9d2b0ab58ab7c505c80f296c558acd85f3f7e3484c249b072c5","schema_version":"1.0","event_id":"sha256:71e6c421b6b9c9d2b0ab58ab7c505c80f296c558acd85f3f7e3484c249b072c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:PG7NCPVLR5UQP5POGUQ3I3YIFI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hofstadter Rules and Generalized Dimensions of the Spectrum of Harper's Equation","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Andreas Rudinger, Frederic Piechon","submitted_at":"1996-10-24T13:34:46Z","abstract_excerpt":"We consider the Harper model which describes two dimensional Bloch electrons in a magnetic field. For irrational flux through the unit-cell the corresponding energy spectrum is known to be a Cantor set with multifractal properties. In order to relate the maximal and minimal fractal dimension of the spectrum of Harper's equation to the irrational number involved, we combine a refined version of the Hofstadter rules with results from semiclassical analysis and tunneling in phase space. For quadratic irrationals $\\omega$ with continued fraction expansion $\\omega = [0;\\overline{n}]$ the maximal fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9610177","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":"2026-05-18T01:07:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6lbYVvJoNNV9FZFy8n28FZtPYsXpud1WjiB2TH/q2MLQxT2BwP6jXedflRPmVdnVYKwN6xo2+2W6rqUDenwKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:26:19.567183Z"},"content_sha256":"4af96bac8d2ed0d4f5bb728611750d87d318e90dcb19f31ee49d9f1b36e557b8","schema_version":"1.0","event_id":"sha256:4af96bac8d2ed0d4f5bb728611750d87d318e90dcb19f31ee49d9f1b36e557b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PG7NCPVLR5UQP5POGUQ3I3YIFI/bundle.json","state_url":"https://pith.science/pith/PG7NCPVLR5UQP5POGUQ3I3YIFI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PG7NCPVLR5UQP5POGUQ3I3YIFI/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":"2026-06-08T19:26:19Z","links":{"resolver":"https://pith.science/pith/PG7NCPVLR5UQP5POGUQ3I3YIFI","bundle":"https://pith.science/pith/PG7NCPVLR5UQP5POGUQ3I3YIFI/bundle.json","state":"https://pith.science/pith/PG7NCPVLR5UQP5POGUQ3I3YIFI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PG7NCPVLR5UQP5POGUQ3I3YIFI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:PG7NCPVLR5UQP5POGUQ3I3YIFI","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":"b6ec50312857f2ed583ae6ac066b65de37e4e44d56cb5662ad7b1240470419d4","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.mes-hall","submitted_at":"1996-10-24T13:34:46Z","title_canon_sha256":"2d63c80c1e2111a29e8ed7cff37409253658310d828e4e0e414e12572f548d3a"},"schema_version":"1.0","source":{"id":"cond-mat/9610177","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9610177","created_at":"2026-05-18T01:07:09Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9610177v1","created_at":"2026-05-18T01:07:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9610177","created_at":"2026-05-18T01:07:09Z"},{"alias_kind":"pith_short_12","alias_value":"PG7NCPVLR5UQ","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"PG7NCPVLR5UQP5PO","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"PG7NCPVL","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:4af96bac8d2ed0d4f5bb728611750d87d318e90dcb19f31ee49d9f1b36e557b8","target":"graph","created_at":"2026-05-18T01:07:09Z","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"},"paper":{"abstract_excerpt":"We consider the Harper model which describes two dimensional Bloch electrons in a magnetic field. For irrational flux through the unit-cell the corresponding energy spectrum is known to be a Cantor set with multifractal properties. In order to relate the maximal and minimal fractal dimension of the spectrum of Harper's equation to the irrational number involved, we combine a refined version of the Hofstadter rules with results from semiclassical analysis and tunneling in phase space. For quadratic irrationals $\\omega$ with continued fraction expansion $\\omega = [0;\\overline{n}]$ the maximal fr","authors_text":"Andreas Rudinger, Frederic Piechon","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.mes-hall","submitted_at":"1996-10-24T13:34:46Z","title":"Hofstadter Rules and Generalized Dimensions of the Spectrum of Harper's Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9610177","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":"sha256:71e6c421b6b9c9d2b0ab58ab7c505c80f296c558acd85f3f7e3484c249b072c5","target":"record","created_at":"2026-05-18T01:07:09Z","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":"b6ec50312857f2ed583ae6ac066b65de37e4e44d56cb5662ad7b1240470419d4","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.mes-hall","submitted_at":"1996-10-24T13:34:46Z","title_canon_sha256":"2d63c80c1e2111a29e8ed7cff37409253658310d828e4e0e414e12572f548d3a"},"schema_version":"1.0","source":{"id":"cond-mat/9610177","kind":"arxiv","version":1}},"canonical_sha256":"79bed13eab8f6907f5ee3521b46f082a0e3c918efe6c7d1bea10cc7c9349dbdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79bed13eab8f6907f5ee3521b46f082a0e3c918efe6c7d1bea10cc7c9349dbdd","first_computed_at":"2026-05-18T01:07:09.187534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:09.187534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wVsOjTvWqXKgCseT9ERA7wY6NzNXx5+/RdVE179HI0Y9/CiAfyuFxs1n7JzP8UE2itd5rQglZp7phSAJk7RaBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:09.187875Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9610177","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71e6c421b6b9c9d2b0ab58ab7c505c80f296c558acd85f3f7e3484c249b072c5","sha256:4af96bac8d2ed0d4f5bb728611750d87d318e90dcb19f31ee49d9f1b36e557b8"],"state_sha256":"e1542e620c8c1e174368fad31b3a5ca63421b9a59c43a1d6e4d8371331c9c7f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BLAiDWRQk0byuNXQnctoeyQWPtrbRC5lU5Ih5OpSBra/U50y/RfY9Zj4ws8RMvrI5w/3TWPj5brm0c3EwWW2Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:26:19.571151Z","bundle_sha256":"ec7673824abc4dc7d020ae73de423dcfbc8e877f377f54eb61c7033000ec576f"}}