{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZIBUV7POIRAIZWPM3IVNEQ5LDU","short_pith_number":"pith:ZIBUV7PO","canonical_record":{"source":{"id":"1702.04337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-02-14T18:49:25Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"e628183f98cca6327d448794bb00f6d79d94710d991710b9790a31a2921fc31f","abstract_canon_sha256":"3a0cf35cf76ebe1e883c2f2c4c90b8489b689b44769c482de5747998a2f704b3"},"schema_version":"1.0"},"canonical_sha256":"ca034afdee44408cd9ecda2ad243ab1d1db0c56939cd9b6c8def1117535fbb9e","source":{"kind":"arxiv","id":"1702.04337","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04337","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04337v1","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04337","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"pith_short_12","alias_value":"ZIBUV7POIRAI","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZIBUV7POIRAIZWPM","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZIBUV7PO","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZIBUV7POIRAIZWPM3IVNEQ5LDU","target":"record","payload":{"canonical_record":{"source":{"id":"1702.04337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-02-14T18:49:25Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"e628183f98cca6327d448794bb00f6d79d94710d991710b9790a31a2921fc31f","abstract_canon_sha256":"3a0cf35cf76ebe1e883c2f2c4c90b8489b689b44769c482de5747998a2f704b3"},"schema_version":"1.0"},"canonical_sha256":"ca034afdee44408cd9ecda2ad243ab1d1db0c56939cd9b6c8def1117535fbb9e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:07.225236Z","signature_b64":"r/7nhxwRk/m4pd+eJkAsTXH3TAfDSO788wyXj7Lw+8rd05v3S0jV45uYJi85lFsOHezSo4GhnQhpvaEXQInlBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca034afdee44408cd9ecda2ad243ab1d1db0c56939cd9b6c8def1117535fbb9e","last_reissued_at":"2026-05-18T00:20:07.224555Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:07.224555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.04337","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":"2026-05-18T00:20:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7rarSTCUzgUabxW6piKjpeqq1w/Sb+CxSU0EfUk06P3D/VbGDg1pa43WWFF3tVu6ujcmIcRCAM5i5w/rOmJpDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:39:28.168778Z"},"content_sha256":"4c7182c269f8b9bdfbe4d4fbc54fee6f2c92969575693c01bdb323c225b0a387","schema_version":"1.0","event_id":"sha256:4c7182c269f8b9bdfbe4d4fbc54fee6f2c92969575693c01bdb323c225b0a387"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZIBUV7POIRAIZWPM3IVNEQ5LDU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral Properties of Continuum Fibonacci Schr\\\"odinger Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.SP","authors_text":"Jake Fillman, May Mei","submitted_at":"2017-02-14T18:49:25Z","abstract_excerpt":"We study continuum Schr\\\"odinger operators on the real line whose potentials are comprised of two compactly supported square-integrable functions concatenated according to an element of the Fibonacci substitution subshift over two letters. We show that the Hausdorff dimension of the spectrum tends to one in the small-coupling and high-energy regimes, regardless of the shape of the potential pieces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04337","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":"2026-05-18T00:20:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XCZd61LMnG42+JRpo4nBQ7kL69aSfolF76HVYfXm1C1N3nyzqP+ZFPFvV7T55s3VHjB0mM3x4Zx1yr6W9iJVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:39:28.169123Z"},"content_sha256":"564360d02b63c707e34d5ab158365ee9b872169fe284833343b8c7eeb677fbfb","schema_version":"1.0","event_id":"sha256:564360d02b63c707e34d5ab158365ee9b872169fe284833343b8c7eeb677fbfb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZIBUV7POIRAIZWPM3IVNEQ5LDU/bundle.json","state_url":"https://pith.science/pith/ZIBUV7POIRAIZWPM3IVNEQ5LDU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZIBUV7POIRAIZWPM3IVNEQ5LDU/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":"2026-06-09T16:39:28Z","links":{"resolver":"https://pith.science/pith/ZIBUV7POIRAIZWPM3IVNEQ5LDU","bundle":"https://pith.science/pith/ZIBUV7POIRAIZWPM3IVNEQ5LDU/bundle.json","state":"https://pith.science/pith/ZIBUV7POIRAIZWPM3IVNEQ5LDU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZIBUV7POIRAIZWPM3IVNEQ5LDU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZIBUV7POIRAIZWPM3IVNEQ5LDU","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":"3a0cf35cf76ebe1e883c2f2c4c90b8489b689b44769c482de5747998a2f704b3","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-02-14T18:49:25Z","title_canon_sha256":"e628183f98cca6327d448794bb00f6d79d94710d991710b9790a31a2921fc31f"},"schema_version":"1.0","source":{"id":"1702.04337","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04337","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04337v1","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04337","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"pith_short_12","alias_value":"ZIBUV7POIRAI","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZIBUV7POIRAIZWPM","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZIBUV7PO","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:564360d02b63c707e34d5ab158365ee9b872169fe284833343b8c7eeb677fbfb","target":"graph","created_at":"2026-05-18T00:20:07Z","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 study continuum Schr\\\"odinger operators on the real line whose potentials are comprised of two compactly supported square-integrable functions concatenated according to an element of the Fibonacci substitution subshift over two letters. We show that the Hausdorff dimension of the spectrum tends to one in the small-coupling and high-energy regimes, regardless of the shape of the potential pieces.","authors_text":"Jake Fillman, May Mei","cross_cats":["math-ph","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-02-14T18:49:25Z","title":"Spectral Properties of Continuum Fibonacci Schr\\\"odinger Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04337","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":"sha256:4c7182c269f8b9bdfbe4d4fbc54fee6f2c92969575693c01bdb323c225b0a387","target":"record","created_at":"2026-05-18T00:20:07Z","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":"3a0cf35cf76ebe1e883c2f2c4c90b8489b689b44769c482de5747998a2f704b3","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-02-14T18:49:25Z","title_canon_sha256":"e628183f98cca6327d448794bb00f6d79d94710d991710b9790a31a2921fc31f"},"schema_version":"1.0","source":{"id":"1702.04337","kind":"arxiv","version":1}},"canonical_sha256":"ca034afdee44408cd9ecda2ad243ab1d1db0c56939cd9b6c8def1117535fbb9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca034afdee44408cd9ecda2ad243ab1d1db0c56939cd9b6c8def1117535fbb9e","first_computed_at":"2026-05-18T00:20:07.224555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:07.224555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r/7nhxwRk/m4pd+eJkAsTXH3TAfDSO788wyXj7Lw+8rd05v3S0jV45uYJi85lFsOHezSo4GhnQhpvaEXQInlBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:07.225236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04337","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c7182c269f8b9bdfbe4d4fbc54fee6f2c92969575693c01bdb323c225b0a387","sha256:564360d02b63c707e34d5ab158365ee9b872169fe284833343b8c7eeb677fbfb"],"state_sha256":"63170ef5f27b22dfed5352bc2a246c10bcf7811862658b4335c270ed96623eae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NFJv8I9suRYC5c+o6RyZtEGt2ZSWYkbHpyRyqESjqRDgIiRHeI0p3aRFJnUZTX3boOWqnnKgvkuO7c4Af4QrCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T16:39:28.171091Z","bundle_sha256":"9a30a73cf8bdba5e98ce05f0b6daede2b47e00f0435675d5cb80367d6dd4a0bd"}}