Pith Number

pith:R73ZDMKQ

pith:2008:R73ZDMKQJVYQPM6XUTA3KKPJGO

not attested not anchored not stored refs pending

Lie coalgebras and rational homotopy theory II: Hopf invariants

Ben Walter, Dev Sinha

arxiv:0809.5084 v5 · 2008-09-29 · 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{R73ZDMKQJVYQPM6XUTA3KKPJGO}

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	2026-05-18T02:24:56.940660Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ff791b1504d7107b3d7a4c1b529e933ac64bc1c6d1dc18d20baed49026a58bc

Aliases

arxiv: 0809.5084 · arxiv_version: 0809.5084v5 · doi: 10.48550/arxiv.0809.5084 · pith_short_12: R73ZDMKQJVYQ · pith_short_16: R73ZDMKQJVYQPM6X · pith_short_8: R73ZDMKQ

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/R73ZDMKQJVYQPM6XUTA3KKPJGO \
  | 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: 8ff791b1504d7107b3d7a4c1b529e933ac64bc1c6d1dc18d20baed49026a58bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53b073453743847869eb548524b3b2eeeb11c1bc2109e64d318afbabf94113be",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2008-09-29T22:23:43Z",
    "title_canon_sha256": "9a0f148ed98c88976779bd82969e02a9e040495d4491cf67ddd5d8b1ddb6c176"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.5084",
    "kind": "arxiv",
    "version": 5
  }
}