Pith Number

pith:4MVMK2PW

pith:2026:4MVMK2PWR34TSSZOB7CLJB3A3H

not attested not anchored not stored refs pending

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations

Jiong-Yue Li

arxiv:2608.00477 v1 · 2026-08-01 · 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{4MVMK2PWR34TSSZOB7CLJB3A3H}

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	2026-08-04T00:36:45.370758Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e32ac569f68ef9394b2e0fc4b48760d9cb065d5bb3cdf6bb05d182ca14518250

Aliases

arxiv: 2608.00477 · arxiv_version: 2608.00477v1 · doi: 10.48550/arxiv.2608.00477 · pith_short_12: 4MVMK2PWR34T · pith_short_16: 4MVMK2PWR34TSSZO · pith_short_8: 4MVMK2PW

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/4MVMK2PWR34TSSZOB7CLJB3A3H \
  | 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: e32ac569f68ef9394b2e0fc4b48760d9cb065d5bb3cdf6bb05d182ca14518250

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9167ea33f06bac37b948940424108ed8817ff1289e942a6d5e514e71d81d7f2b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-08-01T07:05:40Z",
    "title_canon_sha256": "60597067b842565868c06aa987fa47f166c30aa418deb29b535b06dcf4e006b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.00477",
    "kind": "arxiv",
    "version": 1
  }
}