Pith Number

pith:DCOWCJYR

pith:2005:DCOWCJYRASEBGZKLZLLMS57475

not attested not anchored not stored refs pending

The fundamental groups of subsets of closed surfaces inject into their first shape groups

Andreas Zastrow, Hanspeter Fischer

arxiv:math/0512343 v1 · 2005-12-14 · math.GR · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DCOWCJYRASEBGZKLZLLMS57475}

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	2026-05-18T02:41:31.925085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

189d612711048813654bcad6c977fcff586ae3089ff3fcece12de73685618bb2

Aliases

arxiv: math/0512343 · arxiv_version: math/0512343v1 · doi: 10.48550/arxiv.math/0512343 · pith_short_12: DCOWCJYRASEB · pith_short_16: DCOWCJYRASEBGZKL · pith_short_8: DCOWCJYR

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/DCOWCJYRASEBGZKLZLLMS57475 \
  | 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: 189d612711048813654bcad6c977fcff586ae3089ff3fcece12de73685618bb2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "292bb149add76f38d88e09d902d1eedecb177431ad0fffb37b16b84f854bd8fb",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2005-12-14T21:06:31Z",
    "title_canon_sha256": "d26561d3b8c4656731e2edba61ceb25a76fff9e7e74f5b0c892ab65d9adcf9dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0512343",
    "kind": "arxiv",
    "version": 1
  }
}