Pith Number

pith:D4L7TE6N

pith:2011:D4L7TE6NK4N4V2RQ7ULV6O2VKB

not attested not anchored not stored refs pending

Hairiness of $\omega$-bounded surfaces with non-zero Euler characteristic

Alexandre Gabard

arxiv:1103.2062 v1 · 2011-03-10 · 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{D4L7TE6NK4N4V2RQ7ULV6O2VKB}

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	2026-05-18T04:27:03.086398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f17f993cd571bcaea30fd175f3b55505a4c9551bb2b7ab5a28e3d99157748ba

Aliases

arxiv: 1103.2062 · arxiv_version: 1103.2062v1 · doi: 10.48550/arxiv.1103.2062 · pith_short_12: D4L7TE6NK4N4 · pith_short_16: D4L7TE6NK4N4V2RQ · pith_short_8: D4L7TE6N

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/D4L7TE6NK4N4V2RQ7ULV6O2VKB \
  | 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: 1f17f993cd571bcaea30fd175f3b55505a4c9551bb2b7ab5a28e3d99157748ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d30b18a122aafb98dd38e4be1222be1037a28ddb3444373366b45cc8e55c465",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-03-10T15:56:29Z",
    "title_canon_sha256": "15ac4abe7357e07e7ac08ddeb80aa7c04bf0f865d8481da7d3af2bb497731cd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.2062",
    "kind": "arxiv",
    "version": 1
  }
}