Pith Number

pith:GXF4Y24C

pith:2022:GXF4Y24CNDVJ2LDG7SY5JJ35GK

not attested not anchored not stored refs pending

On critical exponential Kirchhoff systems on the Heisenberg group

Du\v{s}an D. Repov\v{s}, Shiqi Li, Sihua Liang

arxiv:2209.05058 v1 · 2022-09-12 · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GXF4Y24CNDVJ2LDG7SY5JJ35GK}

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	2026-07-05T06:11:42.662801Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35cbcc6b8268ea9d2c66fcb1d4a77d32ba37eea15ec5b1067674694cd482f1a7

Aliases

arxiv: 2209.05058 · arxiv_version: 2209.05058v1 · doi: 10.48550/arxiv.2209.05058 · pith_short_12: GXF4Y24CNDVJ · pith_short_16: GXF4Y24CNDVJ2LDG · pith_short_8: GXF4Y24C

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/GXF4Y24CNDVJ2LDG7SY5JJ35GK \
  | 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: 35cbcc6b8268ea9d2c66fcb1d4a77d32ba37eea15ec5b1067674694cd482f1a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45b8eae8909dae924f1c72cbe1a648a74367d1587f146dfcc3a91703bbd72ca8",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2022-09-12T07:30:46Z",
    "title_canon_sha256": "edafeed34e9820a1d18bd9b41b355e8183908edef6a3b0e93bdda763e20989c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2209.05058",
    "kind": "arxiv",
    "version": 1
  }
}