Pith Number

pith:R76KD75K

pith:2015:R76KD75KEX2PS2BN5NYSQPOLXD

not attested not anchored not stored refs pending

Pr\'esentation des groupes de tresses purs et de certaines de leurs extensions

Fran\c{c}ois Digne

arxiv:1511.08731 v3 · 2015-11-27 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R76KD75KEX2PS2BN5NYSQPOLXD}

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	2026-05-18T01:23:15.878565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ffca1ffaa25f4f9682deb71283dcbb8cc17d6f9e769d874dc08b2906ff8250a

Aliases

arxiv: 1511.08731 · arxiv_version: 1511.08731v3 · doi: 10.48550/arxiv.1511.08731 · pith_short_12: R76KD75KEX2P · pith_short_16: R76KD75KEX2PS2BN · pith_short_8: R76KD75K

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/R76KD75KEX2PS2BN5NYSQPOLXD \
  | 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: 8ffca1ffaa25f4f9682deb71283dcbb8cc17d6f9e769d874dc08b2906ff8250a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a357bbc9dc6832bb3e64cccb9c94673a067d8c893b7854897a7fbd31d90421ce",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-11-27T16:34:43Z",
    "title_canon_sha256": "f11f70b6683789b183d42898dbb59ac231cde0f66ff34e175ff3678f9399a791"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.08731",
    "kind": "arxiv",
    "version": 3
  }
}