Pith Number

pith:TWFKVGIS

pith:1999:TWFKVGISOJXCWHI7RFZMKTAJO6

not attested not anchored not stored refs pending

On the imbedding of a finite family of closed disks into a plane or S^{2}

Eugene Polulyakh

arxiv:math/9910108 v1 · 1999-10-21 · math.GT · math.AT · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TWFKVGISOJXCWHI7RFZMKTAJO6}

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	2026-05-18T01:05:32.533493Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d8aaa9912726e2b1d1f8972c54c09779fde7b51a4385b5d4e02fb14ca9afbe5

Aliases

arxiv: math/9910108 · arxiv_version: math/9910108v1 · doi: 10.48550/arxiv.math/9910108 · pith_short_12: TWFKVGISOJXC · pith_short_16: TWFKVGISOJXCWHI7 · pith_short_8: TWFKVGIS

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/TWFKVGISOJXCWHI7RFZMKTAJO6 \
  | 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: 9d8aaa9912726e2b1d1f8972c54c09779fde7b51a4385b5d4e02fb14ca9afbe5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab9186e9a509050d5c1218c4d05b2aaa1de97d08cbba59ff9c61fddc8cea6b99",
    "cross_cats_sorted": [
      "math.AT",
      "math.MG"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1999-10-21T10:52:49Z",
    "title_canon_sha256": "6fc95fca66b39026a59d5a8d9d2ba644b7087ae4ca7f8870d5d22e531a675d43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9910108",
    "kind": "arxiv",
    "version": 1
  }
}