{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CM7APCITRIGC2EJKX2ZLHMY23C","short_pith_number":"pith:CM7APCIT","canonical_record":{"source":{"id":"1203.3646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-16T09:32:22Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"e9f006ee31b89bf548ada834be9ec3fb26ce09d5c304d7f5b8754ccf3923de19","abstract_canon_sha256":"a1efdd81fc88460cc7a562e0b8bfccb76ea39ac3871e102a41761cb6d3d161d5"},"schema_version":"1.0"},"canonical_sha256":"133e0789138a0c2d112abeb2b3b31ad8be7a73fc9bb5aa8a2e8c9cfc7d1f4c78","source":{"kind":"arxiv","id":"1203.3646","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3646","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3646v1","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3646","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"pith_short_12","alias_value":"CM7APCITRIGC","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CM7APCITRIGC2EJK","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CM7APCIT","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CM7APCITRIGC2EJKX2ZLHMY23C","target":"record","payload":{"canonical_record":{"source":{"id":"1203.3646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-16T09:32:22Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"e9f006ee31b89bf548ada834be9ec3fb26ce09d5c304d7f5b8754ccf3923de19","abstract_canon_sha256":"a1efdd81fc88460cc7a562e0b8bfccb76ea39ac3871e102a41761cb6d3d161d5"},"schema_version":"1.0"},"canonical_sha256":"133e0789138a0c2d112abeb2b3b31ad8be7a73fc9bb5aa8a2e8c9cfc7d1f4c78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:50.324437Z","signature_b64":"ccvsJ1/fQmBXZFJ35UVTCO42oK56vKU/4fj/u6zXmXU/1Vs8iiBlCQD/IyW9kcCtrRdbfFNbCyFj7CAxwD7BCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"133e0789138a0c2d112abeb2b3b31ad8be7a73fc9bb5aa8a2e8c9cfc7d1f4c78","last_reissued_at":"2026-05-18T03:59:50.323600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:50.323600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.3646","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":"2026-05-18T03:59:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yKLwDCkW++sNihPusff8UiIk5QTCw+0sSSWixcZVMCcPj0seEvtqpDbX2C+ir/ICODD6trQKYKcerADB7GbtBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:05:18.514808Z"},"content_sha256":"b1161d9b948e6a2031399644105928b2b528aa726034673a1eac233285d65701","schema_version":"1.0","event_id":"sha256:b1161d9b948e6a2031399644105928b2b528aa726034673a1eac233285d65701"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CM7APCITRIGC2EJKX2ZLHMY23C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schroedinger difference equation with deterministic ergodic potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Andras Suto","submitted_at":"2012-03-16T09:32:22Z","abstract_excerpt":"We review the recent developments in the theory of the one-dimensional tight-binding Schr\\\"odinger equation for a class of deterministic ergodic potentials. In the typical examples the potentials are generated by substitutional sequences, like the Fibonacci or the Thue-Morse sequence. We concentrate on rigorous results which will be explained rather than proved. The necessary mathematical background is provided in the text."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3646","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":"2026-05-18T03:59:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xLHhIvj9MPX6i9eeZRaXiqpwf8X7aTZV+v8tkn/amziyBvvKwYiRMYu03yel2mzCGl9FWd88csVYNBN6+oQrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:05:18.515515Z"},"content_sha256":"a9f2c92c3936522a9412a21e61c960434aa65e702ce22f886a670c796acad6db","schema_version":"1.0","event_id":"sha256:a9f2c92c3936522a9412a21e61c960434aa65e702ce22f886a670c796acad6db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CM7APCITRIGC2EJKX2ZLHMY23C/bundle.json","state_url":"https://pith.science/pith/CM7APCITRIGC2EJKX2ZLHMY23C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CM7APCITRIGC2EJKX2ZLHMY23C/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":"2026-05-25T16:05:18Z","links":{"resolver":"https://pith.science/pith/CM7APCITRIGC2EJKX2ZLHMY23C","bundle":"https://pith.science/pith/CM7APCITRIGC2EJKX2ZLHMY23C/bundle.json","state":"https://pith.science/pith/CM7APCITRIGC2EJKX2ZLHMY23C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CM7APCITRIGC2EJKX2ZLHMY23C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CM7APCITRIGC2EJKX2ZLHMY23C","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":"a1efdd81fc88460cc7a562e0b8bfccb76ea39ac3871e102a41761cb6d3d161d5","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-16T09:32:22Z","title_canon_sha256":"e9f006ee31b89bf548ada834be9ec3fb26ce09d5c304d7f5b8754ccf3923de19"},"schema_version":"1.0","source":{"id":"1203.3646","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3646","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3646v1","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3646","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"pith_short_12","alias_value":"CM7APCITRIGC","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CM7APCITRIGC2EJK","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CM7APCIT","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:a9f2c92c3936522a9412a21e61c960434aa65e702ce22f886a670c796acad6db","target":"graph","created_at":"2026-05-18T03:59:50Z","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 review the recent developments in the theory of the one-dimensional tight-binding Schr\\\"odinger equation for a class of deterministic ergodic potentials. In the typical examples the potentials are generated by substitutional sequences, like the Fibonacci or the Thue-Morse sequence. We concentrate on rigorous results which will be explained rather than proved. The necessary mathematical background is provided in the text.","authors_text":"Andras Suto","cross_cats":["cond-mat.stat-mech","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-16T09:32:22Z","title":"Schroedinger difference equation with deterministic ergodic potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3646","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:b1161d9b948e6a2031399644105928b2b528aa726034673a1eac233285d65701","target":"record","created_at":"2026-05-18T03:59:50Z","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":"a1efdd81fc88460cc7a562e0b8bfccb76ea39ac3871e102a41761cb6d3d161d5","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-16T09:32:22Z","title_canon_sha256":"e9f006ee31b89bf548ada834be9ec3fb26ce09d5c304d7f5b8754ccf3923de19"},"schema_version":"1.0","source":{"id":"1203.3646","kind":"arxiv","version":1}},"canonical_sha256":"133e0789138a0c2d112abeb2b3b31ad8be7a73fc9bb5aa8a2e8c9cfc7d1f4c78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"133e0789138a0c2d112abeb2b3b31ad8be7a73fc9bb5aa8a2e8c9cfc7d1f4c78","first_computed_at":"2026-05-18T03:59:50.323600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:50.323600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ccvsJ1/fQmBXZFJ35UVTCO42oK56vKU/4fj/u6zXmXU/1Vs8iiBlCQD/IyW9kcCtrRdbfFNbCyFj7CAxwD7BCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:50.324437Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3646","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1161d9b948e6a2031399644105928b2b528aa726034673a1eac233285d65701","sha256:a9f2c92c3936522a9412a21e61c960434aa65e702ce22f886a670c796acad6db"],"state_sha256":"451ecc5bb8d6c62824642042400034a972e683f1735d8372084940ff208c9044"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Xm53GoSbHJNPfqMgV0ayrpZRpmLgvB8CdbaySMkeQQ9+nnyE88n1kBkTD+Btu5utoxkmV5xfsJLsD4OwKPoAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:05:18.519508Z","bundle_sha256":"6e01ee86df6f924240c7c364724ec67ab5d8b1686eb9935037ca17af636a9d40"}}