pith. sign in
Pith Number

pith:I7CESBOQ

pith:2015:I7CESBOQ2NDHSY5QLVZFDHYZWQ
not attested not anchored not stored refs pending

Mixed spectral types for the one frequency discrete quasi-periodic Schr\"odinger operator

Shiwen Zhang

arxiv:1508.02787 v2 · 2015-08-12 · math.SP · math-ph · math.DS · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?
Add to your LaTeX paper 
\usepackage{pith}
\pithnumber{I7CESBOQ2NDHSY5QLVZFDHYZWQ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp
2 Internet Archive
3 Author claim open · sign in to claim
4 Citations open
5 Replications open
✓ Portable graph bundle live · download bundle · merged state
The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.
Receipt and verification
First computed 2026-05-18T01:35:19.930239Z
Builder pith-number-builder-2026-05-17-v1
Signature Pith Ed25519 (pith-v1-2026-05) · public key
Schema pith-number/v1.0

Canonical hash

47c44905d0d3467963b05d72519f19b43bb29cea396fbf95832e9b04ddbaa7da

Aliases

arxiv: 1508.02787 · arxiv_version: 1508.02787v2 · doi: 10.48550/arxiv.1508.02787 · pith_short_12: I7CESBOQ2NDH · pith_short_16: I7CESBOQ2NDHSY5Q · pith_short_8: I7CESBOQ
Agent API
Resolver JSON Graph JSON Events JSON Schema Signing key
Verify this Pith Number yourself 
curl -sH 'Accept: application/ld+json' https://pith.science/pith/I7CESBOQ2NDHSY5QLVZFDHYZWQ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 47c44905d0d3467963b05d72519f19b43bb29cea396fbf95832e9b04ddbaa7da
Canonical record JSON 
{
  "metadata": {
    "abstract_canon_sha256": "6873bf25584f3d0a553a780449e40a2d718e67a66e6c8dc8ebc362566dfed5a6",
    "cross_cats_sorted": [
      "math-ph",
      "math.DS",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-08-12T00:52:45Z",
    "title_canon_sha256": "53dd878092b0572630c0df04d1c217034c437f63a703aa731fae66f2db0563cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.02787",
    "kind": "arxiv",
    "version": 2
  }
}