Pith Number

pith:VXVUYGQI

pith:2020:VXVUYGQIULV2252GKC32OGOJXO

not attested not anchored not stored refs pending

Sharp decay estimates for massless Dirac fields on a Schwarzschild background

Lin Zhang, Siyuan Ma

arxiv:2008.11429 v2 · 2020-08-26 · math.AP · gr-qc · 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{VXVUYGQIULV2252GKC32OGOJXO}

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	2026-07-05T03:55:24.779295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adeb4c1a08a2ebad774650b7a719c9bbaf79d754f503fcb582f538701788a440

Aliases

arxiv: 2008.11429 · arxiv_version: 2008.11429v2 · doi: 10.48550/arxiv.2008.11429 · pith_short_12: VXVUYGQIULV2 · pith_short_16: VXVUYGQIULV2252G · pith_short_8: VXVUYGQI

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/VXVUYGQIULV2252GKC32OGOJXO \
  | 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: adeb4c1a08a2ebad774650b7a719c9bbaf79d754f503fcb582f538701788a440

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41bcf9845f62fe9ad14f72b0e5c54675354ac28315bc0c9c4edf5f904ae758c9",
    "cross_cats_sorted": [
      "gr-qc",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2020-08-26T07:52:34Z",
    "title_canon_sha256": "c23d4e00741b2bb9b7ce5ee51c158d2955b3ac52b69a239cee87e50f2f2375b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2008.11429",
    "kind": "arxiv",
    "version": 2
  }
}