Pith Number

pith:Q7ULDCZS

pith:2015:Q7ULDCZS3GYSH2SQJB5L6GB5DD

not attested not anchored not stored refs pending

The dual fibration in elementary terms

Anders Kock

arxiv:1501.01947 v1 · 2015-01-08 · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q7ULDCZS3GYSH2SQJB5L6GB5DD}

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	2026-05-18T02:29:45.939524Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87e8b18b32d9b123ea50487abf183d18f56b4ea3d36a2fa6abce124c0cf4d70b

Aliases

arxiv: 1501.01947 · arxiv_version: 1501.01947v1 · doi: 10.48550/arxiv.1501.01947 · pith_short_12: Q7ULDCZS3GYS · pith_short_16: Q7ULDCZS3GYSH2SQ · pith_short_8: Q7ULDCZS

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/Q7ULDCZS3GYSH2SQJB5L6GB5DD \
  | 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: 87e8b18b32d9b123ea50487abf183d18f56b4ea3d36a2fa6abce124c0cf4d70b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14da8413204eb186bb6eeadb67946ddab0c0f492849ef07f0d3e0e1f1e805131",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2015-01-08T20:23:20Z",
    "title_canon_sha256": "13f861e8ac4cd442df5be6c2acfc8331e26eeef224e9c5be46e9b4bc796c4fec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.01947",
    "kind": "arxiv",
    "version": 1
  }
}