Pith Number

pith:F63YTBRV

pith:2014:F63YTBRVFJS4Z7AVFAM4N27VVB

not attested not anchored not stored refs pending

On the equivalence of the definitions of volume of representations

Sungwoon Kim

arxiv:1404.3822 v1 · 2014-04-15 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F63YTBRVFJS4Z7AVFAM4N27VVB}

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	2026-05-18T02:54:13.537270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2fb78986352a65ccfc152819c6ebf5a87a401a10ca449bf1ed2ed4becb3aefcf

Aliases

arxiv: 1404.3822 · arxiv_version: 1404.3822v1 · doi: 10.48550/arxiv.1404.3822 · pith_short_12: F63YTBRVFJS4 · pith_short_16: F63YTBRVFJS4Z7AV · pith_short_8: F63YTBRV

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/F63YTBRVFJS4Z7AVFAM4N27VVB \
  | 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: 2fb78986352a65ccfc152819c6ebf5a87a401a10ca449bf1ed2ed4becb3aefcf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b98a5739d24b956999ea0667ea53d81648e6e05ba5814927fec4391c4fca2992",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-04-15T05:56:57Z",
    "title_canon_sha256": "ba86aeefb18353c0545e6ea7b0c465e4b695f4142bafb0b415cbd9dd5b176bff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.3822",
    "kind": "arxiv",
    "version": 1
  }
}