Pith Number

pith:WPFEWVXN

pith:2015:WPFEWVXNHAI5GZJX4AZUTDM2IX

not attested not anchored not stored refs pending

Topological phase transitions in the 1D multichannel Dirac equation with random mass and a random matrix model

Aur\'elien Grabsch, Christophe Texier

arxiv:1506.05322 v2 · 2015-06-17 · cond-mat.dis-nn · math-ph · 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{WPFEWVXNHAI5GZJX4AZUTDM2IX}

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	2026-05-18T00:58:55.528929Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3ca4b56ed3811d36537e033498d9a45c07fa5fb9c96d53ed1604f8373dc0bcc

Aliases

arxiv: 1506.05322 · arxiv_version: 1506.05322v2 · doi: 10.48550/arxiv.1506.05322 · pith_short_12: WPFEWVXNHAI5 · pith_short_16: WPFEWVXNHAI5GZJX · pith_short_8: WPFEWVXN

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/WPFEWVXNHAI5GZJX4AZUTDM2IX \
  | 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: b3ca4b56ed3811d36537e033498d9a45c07fa5fb9c96d53ed1604f8373dc0bcc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "998633f8c31e8b0f6ed3e78df3678a794ecc603a9756e1ab05daea72b20a41d0",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2015-06-17T13:21:32Z",
    "title_canon_sha256": "4f9047a1aa5a1fd006bafe8773fd6660a87ed113fbd67e971518289be992fd87"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.05322",
    "kind": "arxiv",
    "version": 2
  }
}