Pith Number

pith:X56WRKLS

pith:2018:X56WRKLSLKKBUW4U2KNBAHBMXI

not attested not anchored not stored refs pending

Injectivity in higher order complex domains

Naveen Gupta

arxiv:1810.10707 v1 · 2018-10-22 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X56WRKLSLKKBUW4U2KNBAHBMXI}

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	2026-05-18T00:02:19.823602Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf7d68a9725a941a5b94d29a101c2cba368694e7107fa359e6584c44b88a34a0

Aliases

arxiv: 1810.10707 · arxiv_version: 1810.10707v1 · doi: 10.48550/arxiv.1810.10707 · pith_short_12: X56WRKLSLKKB · pith_short_16: X56WRKLSLKKBUW4U · pith_short_8: X56WRKLS

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/X56WRKLSLKKBUW4U2KNBAHBMXI \
  | 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: bf7d68a9725a941a5b94d29a101c2cba368694e7107fa359e6584c44b88a34a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc57495f7930036024c87b9863f5cf11d621c3d7625ad9a55cd90bceb12e99bd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2018-10-22T13:39:52Z",
    "title_canon_sha256": "c6054949ba4193c47fe9ff37f8a610febd952617c6cbe3353fddc70a6686dd24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.10707",
    "kind": "arxiv",
    "version": 1
  }
}