Pith Number

pith:K2AM5W6Y

pith:2015:K2AM5W6YN2XSRV6QLDRIFZTPE5

not attested not anchored not stored refs pending

Systolic volume and complexity of 3-manifolds

Lizhi Chen

arxiv:1509.07647 v4 · 2015-09-25 · 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{K2AM5W6YN2XSRV6QLDRIFZTPE5}

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	2026-07-05T00:11:52.873237Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5680cedbd86eaf28d7d058e282e66f2761876d72fe0b93bad64f32f9bb9ebcd3

Aliases

arxiv: 1509.07647 · arxiv_version: 1509.07647v4 · doi: 10.48550/arxiv.1509.07647 · pith_short_12: K2AM5W6YN2XS · pith_short_16: K2AM5W6YN2XSRV6Q · pith_short_8: K2AM5W6Y

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/K2AM5W6YN2XSRV6QLDRIFZTPE5 \
  | 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: 5680cedbd86eaf28d7d058e282e66f2761876d72fe0b93bad64f32f9bb9ebcd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a95e460e1bd14a449aaa3a258c4613655447231c32bbb09d9459ad45495baded",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-09-25T09:23:00Z",
    "title_canon_sha256": "c7b1574472f474df14b926be4703aebc5e2359878977d4478c214b6f9f09a4a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07647",
    "kind": "arxiv",
    "version": 4
  }
}