Pith Number

pith:RZDDJO6W

pith:2017:RZDDJO6WOG4TMI4M2IE2JWFJ2T

not attested not anchored not stored refs pending

Spectral bounds for the torsion function

Michiel van den Berg

arxiv:1701.02172 v2 · 2017-01-09 · math.SP · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RZDDJO6WOG4TMI4M2IE2JWFJ2T}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T00:47:37.945776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8e4634bbd671b936238cd209a4d8a9d4f16ffc6d71580733c5222e18b9fc45a9

Aliases

arxiv: 1701.02172 · arxiv_version: 1701.02172v2 · doi: 10.48550/arxiv.1701.02172 · pith_short_12: RZDDJO6WOG4T · pith_short_16: RZDDJO6WOG4TMI4M · pith_short_8: RZDDJO6W

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/RZDDJO6WOG4TMI4M2IE2JWFJ2T \
  | 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: 8e4634bbd671b936238cd209a4d8a9d4f16ffc6d71580733c5222e18b9fc45a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1cdcf1c29571376757ac47749faec0e82547ae71c95f146cc29f140b6a420233",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2017-01-09T13:40:39Z",
    "title_canon_sha256": "b89c8305df07b8fe4d7dbbcd6476e045f26e52de64b9ab44548b38a4dee32479"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.02172",
    "kind": "arxiv",
    "version": 2
  }
}