Pith Number

pith:3Y76JANN

pith:2016:3Y76JANNPN6KMSNJPEQCYNBW2M

not attested not anchored not stored refs pending

The triviality of the 61-stem in the stable homotopy groups of spheres

Guozhen Wang, Zhouli Xu

arxiv:1601.02184 v4 · 2016-01-10 · math.AT · math.DG · 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{3Y76JANNPN6KMSNJPEQCYNBW2M}

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	2026-05-18T00:42:24.075705Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de3fe481ad7b7ca649a979202c3436d3351fa5be0785b12e71e22620c4c8a660

Aliases

arxiv: 1601.02184 · arxiv_version: 1601.02184v4 · doi: 10.48550/arxiv.1601.02184 · pith_short_12: 3Y76JANNPN6K · pith_short_16: 3Y76JANNPN6KMSNJ · pith_short_8: 3Y76JANN

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/3Y76JANNPN6KMSNJPEQCYNBW2M \
  | 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: de3fe481ad7b7ca649a979202c3436d3351fa5be0785b12e71e22620c4c8a660

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c278012ae510b7ffc2dda4410900b1f6a3b8ab71a9ded686b51935bdab1af3bf",
    "cross_cats_sorted": [
      "math.DG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-01-10T07:29:46Z",
    "title_canon_sha256": "a2d1bacb5026b40ce2ab624a5b5a7788f61bf69ed440e9667d6c7cc212a7b956"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.02184",
    "kind": "arxiv",
    "version": 4
  }
}