Pith Number

pith:CRL6XDAK

pith:1997:CRL6XDAKD7V3HQYIWX2ACWGGU3

not attested not anchored not stored refs pending

Alexander duality, gropes and link homotopy

Peter Teichner, Vyacheslav S. Krushkal

arxiv:math/9705222 v3 · 1997-05-28 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CRL6XDAKD7V3HQYIWX2ACWGGU3}

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	2026-05-18T02:37:59.364109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1457eb8c0a1febb3c308b5f40158c6a6fb4e546c7217b379401c53dda4b4eaf1

Aliases

arxiv: math/9705222 · arxiv_version: math/9705222v3 · doi: 10.48550/arxiv.math/9705222 · pith_short_12: CRL6XDAKD7V3 · pith_short_16: CRL6XDAKD7V3HQYI · pith_short_8: CRL6XDAK

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/CRL6XDAKD7V3HQYIWX2ACWGGU3 \
  | 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: 1457eb8c0a1febb3c308b5f40158c6a6fb4e546c7217b379401c53dda4b4eaf1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21259da48b0d6afb704c6c0c993eb4b397ecd36b2fa376be88b945026e3588ba",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1997-05-28T00:00:00Z",
    "title_canon_sha256": "2024b74a4cb58dcc3313df9eae0e70f492d24eefe0f7064a8cf008aab152b823"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9705222",
    "kind": "arxiv",
    "version": 3
  }
}