Pith Number

pith:LHVI4GGN

pith:2015:LHVI4GGNS6XCVDIVR7AKQTD6X2

not attested not anchored not stored refs pending

On an injectivity lemma in the proof of Tannakian duality

Ph\`ung H\^o Hai

arxiv:1510.02714 v1 · 2015-10-09 · math.RA · math.CT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LHVI4GGNS6XCVDIVR7AKQTD6X2}

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	2026-05-18T00:43:21.288628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59ea8e18cd97ae2a8d158fc0a84c7ebebf9a721b2f119cb7825ae6bdd68a4d6b

Aliases

arxiv: 1510.02714 · arxiv_version: 1510.02714v1 · doi: 10.48550/arxiv.1510.02714 · pith_short_12: LHVI4GGNS6XC · pith_short_16: LHVI4GGNS6XCVDIV · pith_short_8: LHVI4GGN

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/LHVI4GGNS6XCVDIVR7AKQTD6X2 \
  | 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: 59ea8e18cd97ae2a8d158fc0a84c7ebebf9a721b2f119cb7825ae6bdd68a4d6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "baf267de106b0e78f05764a4a1c34d572aeb89e66658a09590b7723b3db0e4ad",
    "cross_cats_sorted": [
      "math.CT",
      "math.RT"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2015-10-09T15:59:45Z",
    "title_canon_sha256": "c1e175543637eb9ad0d67f0c87df7ba4a641b5797101a24886b4641afb76ff19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.02714",
    "kind": "arxiv",
    "version": 1
  }
}