Pith Number

pith:ZKYWUQYW

pith:1996:ZKYWUQYW2Z2CL5GQSEJ4FF7LVR

not attested not anchored not stored refs pending

Ping-Pong on Negatively Curved Groups

Rita Gitik

arxiv:math/9612211 v1 · 1996-12-03 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZKYWUQYW2Z2CL5GQSEJ4FF7LVR}

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	2026-05-18T01:05:37.390468Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cab16a4316d67425f4d09113c297ebac651b79d92c4cdd42835f6f141ec6a153

Aliases

arxiv: math/9612211 · arxiv_version: math/9612211v1 · doi: 10.48550/arxiv.math/9612211 · pith_short_12: ZKYWUQYW2Z2C · pith_short_16: ZKYWUQYW2Z2CL5GQ · pith_short_8: ZKYWUQYW

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/ZKYWUQYW2Z2CL5GQSEJ4FF7LVR \
  | 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: cab16a4316d67425f4d09113c297ebac651b79d92c4cdd42835f6f141ec6a153

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee130ff158920aa229e60e737b18390c053aefc10adc895cfbac2539760bb945",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "1996-12-03T00:00:00Z",
    "title_canon_sha256": "b25b1943a0e2b9e458dd8548f86f27c4431dc8d36df8a94097fc06542bbf6344"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9612211",
    "kind": "arxiv",
    "version": 1
  }
}