Pith Number

pith:GRBVGW2I

pith:2013:GRBVGW2I2VMJNIVTSEUZTD5UPG

not attested not anchored not stored refs pending

Existence of solution to a critical trace equation with variable exponent

Analia Silva, Julian Fernandez Bonder, Nicolas Saintier

arxiv:1301.2962 v1 · 2013-01-14 · 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{GRBVGW2I2VMJNIVTSEUZTD5UPG}

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	2026-05-18T03:36:27.715114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3443535b48d55896a2b39129998fb4799f96e62f4f010a65a45cfa0e7fcac410

Aliases

arxiv: 1301.2962 · arxiv_version: 1301.2962v1 · doi: 10.48550/arxiv.1301.2962 · pith_short_12: GRBVGW2I2VMJ · pith_short_16: GRBVGW2I2VMJNIVT · pith_short_8: GRBVGW2I

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/GRBVGW2I2VMJNIVTSEUZTD5UPG \
  | 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: 3443535b48d55896a2b39129998fb4799f96e62f4f010a65a45cfa0e7fcac410

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21b57dcc4f646082f7f84485e26c66a8b920f14c0ec8c00e0077318747e69aa6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-01-14T13:04:05Z",
    "title_canon_sha256": "e5cdf1619996fd76ebbee1f4363261b87b9ac8ff546e8ffbb1dd80a015267476"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.2962",
    "kind": "arxiv",
    "version": 1
  }
}