Pith Number

pith:TWN33WIM

pith:2019:TWN33WIMYKVKGKTEVGFH3ANXU7

not attested not anchored not stored refs pending

An existence theory for nonlinear equations on metric graphs via energy methods

Matthias Hofmann

arxiv:1909.07856 v2 · 2019-09-17 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TWN33WIMYKVKGKTEVGFH3ANXU7}

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	2026-07-05T01:17:24.844965Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d9bbdd90cc2aaa32a64a98a7d81b7a7ddc28ebb289c021dce5330f7ecadb25f

Aliases

arxiv: 1909.07856 · arxiv_version: 1909.07856v2 · doi: 10.48550/arxiv.1909.07856 · pith_short_12: TWN33WIMYKVK · pith_short_16: TWN33WIMYKVKGKTE · pith_short_8: TWN33WIM

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/TWN33WIMYKVKGKTEVGFH3ANXU7 \
  | 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: 9d9bbdd90cc2aaa32a64a98a7d81b7a7ddc28ebb289c021dce5330f7ecadb25f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8756901c54adb5435f5c9172963eebcf5c8c07080586aec796a65382aee693c2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-09-17T14:45:41Z",
    "title_canon_sha256": "48045c071b9c68f2ec246cb8d01ae7462002c4260e8103cf7c8813cf5f2bde0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.07856",
    "kind": "arxiv",
    "version": 2
  }
}