Pith Number

pith:TFXF2YFX

pith:2021:TFXF2YFXAVK4KJ7LWJ4XKQ3LP3

not attested not anchored not stored refs pending

Normalized ground states for Kirchhoff equations in ${\mathbb{R}}^{3}$ with a critical nonlinearity

Penghui Zhang, Zhiqing Han

arxiv:2103.07174 v1 · 2021-03-12 · 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{TFXF2YFXAVK4KJ7LWJ4XKQ3LP3}

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	2026-07-05T03:57:07.417186Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

996e5d60b70555c527ebb27975436b7ec4cd6ba05cfa36453cd75c4724de9dde

Aliases

arxiv: 2103.07174 · arxiv_version: 2103.07174v1 · doi: 10.48550/arxiv.2103.07174 · pith_short_12: TFXF2YFXAVK4 · pith_short_16: TFXF2YFXAVK4KJ7L · pith_short_8: TFXF2YFX

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/TFXF2YFXAVK4KJ7LWJ4XKQ3LP3 \
  | 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: 996e5d60b70555c527ebb27975436b7ec4cd6ba05cfa36453cd75c4724de9dde

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7507e3fe222a7908635eed9fa30d4404ec6cbc9e1bc422f94a89f26356aa6cc4",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-03-12T09:51:29Z",
    "title_canon_sha256": "2c1f927a7f8f449e2d7c83a6393528a99808e459f44199e0c759ae47794c80e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.07174",
    "kind": "arxiv",
    "version": 1
  }
}