Pith Number

pith:PTK7X2UH

pith:2019:PTK7X2UH5HFUO6ZM3ZY2UCGA7F

not attested not anchored not stored refs pending

The affine-null formulation of the gravitational equations: spherical case

H. P. de Oliveira, J. A. Crespo, J. Winicour

arxiv:1910.03439 v1 · 2019-10-08 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PTK7X2UH5HFUO6ZM3ZY2UCGA7F}

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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.

Cited by

1 paper in Pith

Conformal compactification and affine-null metric formulation of the Einstein equations

Receipt and verification

First computed	2026-07-05T00:18:41.179756Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cd5fbea87e9cb477b2cde71aa08c0f96213af60dcd0189162f8764d0e67ad5f

Aliases

arxiv: 1910.03439 · arxiv_version: 1910.03439v1 · doi: 10.48550/arxiv.1910.03439 · pith_short_12: PTK7X2UH5HFU · pith_short_16: PTK7X2UH5HFUO6ZM · pith_short_8: PTK7X2UH

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/PTK7X2UH5HFUO6ZM3ZY2UCGA7F \
  | 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: 7cd5fbea87e9cb477b2cde71aa08c0f96213af60dcd0189162f8764d0e67ad5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1058e7815b35a3f173db2967c4ac4166916661b384ff9aed1f48ee5c3e9dda6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2019-10-08T14:57:49Z",
    "title_canon_sha256": "0ff84e6cf6e1113e5e90a92dbb21a7c6e320e99dc30a717923c3639d1c08d4ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1910.03439",
    "kind": "arxiv",
    "version": 1
  }
}