Pith Number

pith:MFRXYMU7

pith:2026:MFRXYMU7H5CTA2MCV2UKHXERJF

not attested not anchored not stored refs resolved

Fields where torsion forms decompose

Karim Johannes Becher, M. Archita

Over real fields that are transcendence degree one extensions of hereditarily Pythagorean bases, every torsion quadratic form decomposes into an orthogonal sum of 2-dimensional torsion forms.

arxiv:2605.13844 v1 · 2026-05-13 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MFRXYMU7H5CTA2MCV2UKHXERJF}

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.

Claims

C1strongest claim

Over a real field which is an extension of transcendence degree 1 of a hereditarily pythagorean base field, every quadratic form which is torsion decomposes into an orthogonal sum of 2-dimensional torsion forms.

C2weakest assumption

The base field is hereditarily Pythagorean and the extension has transcendence degree exactly 1 while remaining real; if the hereditarily Pythagorean condition fails or the degree is higher, the decomposition may not hold.

C3one line summary

Torsion quadratic forms over real fields of transcendence degree 1 over hereditarily Pythagorean bases decompose into orthogonal sums of 2-dimensional torsion forms.

References

12 extracted · 12 resolved · 0 Pith anchors

[1] J. K. Arason, A. Pfister. Zur Theorie der quadratischen Formen ¨ uber formalreellen K¨ orpern.Math. Z. 153 (1977), 289–296 1977

[2] K.J. Becher. Minimal weakly isotropic forms. Math. Z., 252 (2006), 91–102 2006

[3] K.J. Becher, N. Daans, Ph. Dittmann. Uniform existential definitions of valuations in function fields in one variable. Preprint (2025), https://arxiv.org/abs/2311.06044 2025

[4] K.J. Becher, N. Daans, D. Grimm, G. Manzano-Flores, M. Zaninelli. The Pythagoras number of function fields. Preprint (2024), https://arxiv.org/abs/2302.11425 2024

[5] K.J. Becher, N. Daans, V. Mehmeti. The u-invariant of function fields in one variable. Preprint (2025), https://arxiv.org/abs/2502.13086 2025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:09.381769Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61637c329f3f45306982aea8a3dc91496e91248d22e4292f6821709ea5b37c22

Aliases

arxiv: 2605.13844 · arxiv_version: 2605.13844v1 · doi: 10.48550/arxiv.2605.13844 · pith_short_12: MFRXYMU7H5CT · pith_short_16: MFRXYMU7H5CTA2MC · pith_short_8: MFRXYMU7

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/MFRXYMU7H5CTA2MCV2UKHXERJF \
  | 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: 61637c329f3f45306982aea8a3dc91496e91248d22e4292f6821709ea5b37c22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3a6b97133cf25cbd3256e3828ccb10cb7f19d10d032dbc8949e1d8f84e923c9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-13T17:59:30Z",
    "title_canon_sha256": "af2b0c0e513247cf44c27e5d60aa57ad7a9c95ffaacf9567b414cba161c4eecd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13844",
    "kind": "arxiv",
    "version": 1
  }
}