Pith Number

pith:2PZASCY3

pith:2017:2PZASCY3GB6HW6BS6JU67XGZTV

not attested not anchored not stored refs pending

On Euler characteristic and fundamental groups of compact manifolds

Bing-Long Chen, Xiaokui Yang

arxiv:1711.03309 v2 · 2017-11-09 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2PZASCY3GB6HW6BS6JU67XGZTV}

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	2026-05-18T00:22:18.585288Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3f2090b1b307c7b7832f269efdcd99d5f6cd00906250fe8457a9c60d0a42928

Aliases

arxiv: 1711.03309 · arxiv_version: 1711.03309v2 · doi: 10.48550/arxiv.1711.03309 · pith_short_12: 2PZASCY3GB6H · pith_short_16: 2PZASCY3GB6HW6BS · pith_short_8: 2PZASCY3

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/2PZASCY3GB6HW6BS6JU67XGZTV \
  | 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: d3f2090b1b307c7b7832f269efdcd99d5f6cd00906250fe8457a9c60d0a42928

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60c10eeb953159d5207e7352fa3c835108c15036265eab0df9c460fa10d146fd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-11-09T10:12:54Z",
    "title_canon_sha256": "1f5eae9bcdd1a3aa6ba65d4ff2d406863aadb12ef048c7e93a5666f157e99e3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.03309",
    "kind": "arxiv",
    "version": 2
  }
}