Pith Number

pith:U3Y5VDKB

pith:2013:U3Y5VDKBY4M2D42DSJLOECGOBR

not attested not anchored not stored refs pending

Anderson localization for the completely resonant phases

Wencai Liu, Xiaoping Yuan

arxiv:1311.0862 v1 · 2013-11-04 · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U3Y5VDKBY4M2D42DSJLOECGOBR}

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	2026-05-18T00:17:55.665783Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6f1da8d41c719a1f3439256e208ce0c6e276361bf4aebb75b54fb6025f3c5ac

Aliases

arxiv: 1311.0862 · arxiv_version: 1311.0862v1 · doi: 10.48550/arxiv.1311.0862 · pith_short_12: U3Y5VDKBY4M2 · pith_short_16: U3Y5VDKBY4M2D42D · pith_short_8: U3Y5VDKB

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/U3Y5VDKBY4M2D42DSJLOECGOBR \
  | 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: a6f1da8d41c719a1f3439256e208ce0c6e276361bf4aebb75b54fb6025f3c5ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65f2625eac0fc985030e82d2deb9f0e692132fda57892fccac3020dcf1fa99a3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-11-04T12:42:02Z",
    "title_canon_sha256": "f2177f415cee00f957d53f983bc91c38e191a5947e46abcacda9d19925a9db18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.0862",
    "kind": "arxiv",
    "version": 1
  }
}