Pith Number

pith:U6DKPNUL

pith:2012:U6DKPNULYS2XY6RV2LDZY4VWLG

not attested not anchored not stored refs pending

Existence of nodal solutions for Dirac equations with singular nonlinearities

Lo\"ic Le Treust (CEREMADE)

arxiv:1208.2453 v2 · 2012-08-12 · math.AP · 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{U6DKPNULYS2XY6RV2LDZY4VWLG}

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	2026-05-18T03:36:06.347811Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a786a7b68bc4b57c7a35d2c79c72b659a9b9297fc64dd33c8bba6e3016e853b4

Aliases

arxiv: 1208.2453 · arxiv_version: 1208.2453v2 · doi: 10.48550/arxiv.1208.2453 · pith_short_12: U6DKPNULYS2X · pith_short_16: U6DKPNULYS2XY6RV · pith_short_8: U6DKPNUL

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/U6DKPNULYS2XY6RV2LDZY4VWLG \
  | 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: a786a7b68bc4b57c7a35d2c79c72b659a9b9297fc64dd33c8bba6e3016e853b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd3e0f1b433d64fb93629adb11290bb94ae8f0d98bd8c1df74d5ca2a7011ab06",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-08-12T19:23:17Z",
    "title_canon_sha256": "11472636c8c50d6b0657525e578a2701138d266a4fb7cff3ce70064ae7c38004"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.2453",
    "kind": "arxiv",
    "version": 2
  }
}