Pith Number

pith:NE6GA7HK

pith:2002:NE6GA7HKKQJD4VZHMWIXV5IZ5D

not attested not anchored not stored refs pending

Algebraic topology and modular forms

Michael J. Hopkins

arxiv:math/0212397 v1 · 2002-12-01 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NE6GA7HKKQJD4VZHMWIXV5IZ5D}

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.

Cited by

1 paper in Pith

Flux Quantization of Type IIA in Unstable K-Theory

Receipt and verification

First computed	2026-07-04T14:36:52.134170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

693c607cea54123e572765917af519e8e582f655cbee2e90dd1f0c858d2272ee

Aliases

arxiv: math/0212397 · arxiv_version: math/0212397v1 · doi: 10.48550/arxiv.math/0212397 · pith_short_12: NE6GA7HKKQJD · pith_short_16: NE6GA7HKKQJD4VZH · pith_short_8: NE6GA7HK

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/NE6GA7HKKQJD4VZHMWIXV5IZ5D \
  | 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: 693c607cea54123e572765917af519e8e582f655cbee2e90dd1f0c858d2272ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52b72932375df713f53f7bb1c93c7abc7d3bbc19a3d151a2f0ca7aa73d6ca3f3",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AT",
    "submitted_at": "2002-12-01T00:00:00Z",
    "title_canon_sha256": "47118be161ffb7e9d8b8fdc628f81cdc7fbace701b790a60c1db0faa7873551e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0212397",
    "kind": "arxiv",
    "version": 1
  }
}