Pith Number

pith:SWQJDWBS

pith:1998:SWQJDWBSCTPSRA2SRVEAA7GRHC

not attested not anchored not stored refs pending

Examples of non-trivial roots of unity at ideal points of hyperbolic 3-manifolds

Nathan M. Dunfield

arxiv:math/9801064 v2 · 1998-01-13 · 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{SWQJDWBSCTPSRA2SRVEAA7GRHC}

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	2026-07-04T14:40:25.183257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

95a091d83214df2883528d48007cd1389fddd14f92974ecb74de70c47e06feb3

Aliases

arxiv: math/9801064 · arxiv_version: math/9801064v2 · doi: 10.48550/arxiv.math/9801064 · pith_short_12: SWQJDWBSCTPS · pith_short_16: SWQJDWBSCTPSRA2S · pith_short_8: SWQJDWBS

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/SWQJDWBSCTPSRA2SRVEAA7GRHC \
  | 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: 95a091d83214df2883528d48007cd1389fddd14f92974ecb74de70c47e06feb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "803663ff09e7b5a52cc5464720cd18259822c554e6fbd27bd2732476e0f95144",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1998-01-13T16:16:33Z",
    "title_canon_sha256": "3158cbc999c139b71ee656be478cbafc2a135af4545ee955f97d292006b6cb20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9801064",
    "kind": "arxiv",
    "version": 2
  }
}