Pith Number

pith:QW5QW3OO

pith:2010:QW5QW3OO7ML36S3T24KDNVGJLZ

not attested not anchored not stored refs pending

Quantum Gravity via Manifold Positivity

Michael Freedman

arxiv:1008.1045 v3 · 2010-08-05 · quant-ph · gr-qc · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QW5QW3OO7ML36S3T24KDNVGJLZ}

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	2026-05-18T04:34:19.339644Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85bb0b6dcefb17bf4b73d71436d4c95e795943a30f0bf16c01cad93bd5af3bea

Aliases

arxiv: 1008.1045 · arxiv_version: 1008.1045v3 · doi: 10.48550/arxiv.1008.1045 · pith_short_12: QW5QW3OO7ML3 · pith_short_16: QW5QW3OO7ML36S3T · pith_short_8: QW5QW3OO

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/QW5QW3OO7ML36S3T24KDNVGJLZ \
  | 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: 85bb0b6dcefb17bf4b73d71436d4c95e795943a30f0bf16c01cad93bd5af3bea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9ecf3b14229d79c4e7b73a6e65e75b0c23cdbddeffd3d770c43780b7342a6a1",
    "cross_cats_sorted": [
      "gr-qc",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2010-08-05T19:28:25Z",
    "title_canon_sha256": "6a10d37baad137279afd2f063162b2da0181fd497bc51876edb9ec721e37c035"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.1045",
    "kind": "arxiv",
    "version": 3
  }
}