Pith Number

pith:APJJ6YNX

pith:2004:APJJ6YNXVZIUVS3UXVRLWLGQYM

not attested not anchored not stored refs pending

Regularity Theorems and Energy Identities for Dirac-Harmonic Maps

Guofang Wang, Jiayu Li, Juergen Jost, Qun Chen

arxiv:math/0411327 v1 · 2004-11-15 · math.DG · 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{APJJ6YNXVZIUVS3UXVRLWLGQYM}

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	2026-07-04T14:39:22.544548Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03d29f61b7ae514acb74bd62bb2cd0c3061a7d4cc60c6497fd69705dd6e5b0d2

Aliases

arxiv: math/0411327 · arxiv_version: math/0411327v1 · doi: 10.48550/arxiv.math/0411327 · pith_short_12: APJJ6YNXVZIU · pith_short_16: APJJ6YNXVZIUVS3U · pith_short_8: APJJ6YNX

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/APJJ6YNXVZIUVS3UXVRLWLGQYM \
  | 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: 03d29f61b7ae514acb74bd62bb2cd0c3061a7d4cc60c6497fd69705dd6e5b0d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ca2927616eaa577d7ce766792763ad8dc0870c54cfd63a85de3525aa61d3a27",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2004-11-15T13:22:10Z",
    "title_canon_sha256": "e2106adaa5354e883d47658c74f5a6cab690cdf0643d92534a9d9288a21883f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0411327",
    "kind": "arxiv",
    "version": 1
  }
}