Pith Number

pith:NA77KAEA

pith:2016:NA77KAEADPISDMIJKUFGVBW2EV

not attested not anchored not stored refs pending

Uniform fellow traveling between surgery paths in the sphere graph

Kasra Rafi, Matt Clay, Yulan Qing

arxiv:1610.05832 v3 · 2016-10-19 · math.GR · 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{NA77KAEADPISDMIJKUFGVBW2EV}

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	2026-05-18T00:20:57.098414Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

683ff500801bd121b109550a6a86da2574af9d89216513e9407e2241226f76c7

Aliases

arxiv: 1610.05832 · arxiv_version: 1610.05832v3 · doi: 10.48550/arxiv.1610.05832 · pith_short_12: NA77KAEADPIS · pith_short_16: NA77KAEADPISDMIJ · pith_short_8: NA77KAEA

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/NA77KAEADPISDMIJKUFGVBW2EV \
  | 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: 683ff500801bd121b109550a6a86da2574af9d89216513e9407e2241226f76c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "572d266e64132628fbcd6a98ccb107adba1ecca602d66dd18a7b6b32ded204db",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-10-19T00:26:03Z",
    "title_canon_sha256": "ae3a4fc4daedb7309fcf1e2d62716bc91ad440eec8e0c8435c38dd2b3b4be8fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.05832",
    "kind": "arxiv",
    "version": 3
  }
}