Pith Number

pith:YXJWJG3X

pith:2017:YXJWJG3XQ6434MEAQ26D772F2F

not attested not anchored not stored refs pending

Global existence of Dirac-wave maps with curvature term on expanding spacetimes

Klaus Kroencke, Volker Branding

arxiv:1709.06520 v2 · 2017-09-19 · math.DG · math-ph · math.AP · 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{YXJWJG3XQ6434MEAQ26D772F2F}

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	2026-05-18T00:10:19.244806Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5d3649b7787b9be308086bc3fff45d164bde5c661c04b1975aaee2af5ade10e

Aliases

arxiv: 1709.06520 · arxiv_version: 1709.06520v2 · doi: 10.48550/arxiv.1709.06520 · pith_short_12: YXJWJG3XQ643 · pith_short_16: YXJWJG3XQ6434MEA · pith_short_8: YXJWJG3X

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/YXJWJG3XQ6434MEAQ26D772F2F \
  | 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: c5d3649b7787b9be308086bc3fff45d164bde5c661c04b1975aaee2af5ade10e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23428f27a54e33871fcc6e77b83d233b495c77f028970e5059fa796588ac04e0",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-09-19T16:38:53Z",
    "title_canon_sha256": "b2e0687ea6a20445704a72fc41aad15b97d0b367a8077ad0029ba0c2bd6cd034"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.06520",
    "kind": "arxiv",
    "version": 2
  }
}