Pith Number

pith:YNWGYRWX

pith:2015:YNWGYRWXEDWC3BAVYNPIOQVMTE

not attested not anchored not stored refs pending

Norms on the cohomology of hyperbolic 3-manifolds

Jeffrey F. Brock, Nathan M. Dunfield

arxiv:1510.06292 v5 · 2015-10-21 · math.GT · math.DG · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YNWGYRWXEDWC3BAVYNPIOQVMTE}

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	2026-05-18T00:20:27.824619Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c36c6c46d720ec2d8415c35e8742ac991746d30368f5ff630df75a1d958a78e1

Aliases

arxiv: 1510.06292 · arxiv_version: 1510.06292v5 · doi: 10.48550/arxiv.1510.06292 · pith_short_12: YNWGYRWXEDWC · pith_short_16: YNWGYRWXEDWC3BAV · pith_short_8: YNWGYRWX

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/YNWGYRWXEDWC3BAVYNPIOQVMTE \
  | 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: c36c6c46d720ec2d8415c35e8742ac991746d30368f5ff630df75a1d958a78e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d84ccd4f7714b949689d8aa41842f1e03bc97261d90f26cea37dd8d2a2fd45e",
    "cross_cats_sorted": [
      "math.DG",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-10-21T15:13:01Z",
    "title_canon_sha256": "a431692568878f3810adc2703a3a640960d4146a4018b1bb400f9b34ea8a17e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.06292",
    "kind": "arxiv",
    "version": 5
  }
}