Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-12T16:36:14.907586Z
Paper Citation Record · LEDGER
Heights and morphisms in number fields
As of 13 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2411.13522.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
40 of 40 outbound references displayed
- verified exact7
- verified fuzzy24
- unresolved9
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 22bda09d-d921-46e8-a872-4b5f21e34cd1 · outbound
This paper cites Axiomatic characterization of fields by the product formula for valuations.
Heights and morphisms in number fields Axiomatic characterization of fields by the product formula for valuations
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.763230Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation abf3645d-0106-43bb-ad6b-10696723f539 · outbound
This paper cites Silverman, and Thomas J.
Heights and morphisms in number fields Silverman, and Thomas J
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.746313Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation ebfb2f98-972d-4a49-8b34-3b0b5f2c3392 · outbound
This paper cites Call and Joseph H.
Heights and morphisms in number fields Call and Joseph H
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.730538Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4557cd2a-55c2-4c86-8113-1ef59ae0a7ee · outbound
This paper cites an unresolved cited work.
Heights and morphisms in number fields Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T16:36:15.711996Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation b5abb8bd-5301-47ea-ac23-6f76d4c50b06 · outbound
This paper cites Lectures on height zeta functions: At the confluence of algebraic geometry, al- gebraic number theory, and analysis.
Heights and morphisms in number fields Lectures on height zeta functions: At the confluence of algebraic geometry, al- gebraic number theory, and analysis
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.690102Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation f3bef3d8-d761-448a-b12b-f4e8469ac332 · outbound
This paper cites an unresolved cited work.
Heights and morphisms in number fields Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T16:36:15.672974Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 53869f0d-5cd9-4cbe-b0e5-8d2c2ec98f37 · outbound
This paper cites Cox, John Little, and Donal O’Shea.
Heights and morphisms in number fields Cox, John Little, and Donal O’Shea
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.655943Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 1005c412-eba8-42c9-aba4-69c6998f93aa · outbound
This paper cites Regularity of Dynamical Green’s Functions.
Heights and morphisms in number fields Regularity of Dynamical Green’s Functions
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.639332Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 3268e1d3-59d7-4763-ab43-f70440b52142 · outbound
This paper cites Rational points of projective spaces over rings.
Heights and morphisms in number fields Rational points of projective spaces over rings
Reference 9
- Resolution
- verified exact
- raw_fallback, observed 2026-08-12T16:36:15.199630Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation b0c2235a-3215-437c-a90a-def1ede0a1b7 · outbound
This paper cites Manin, and Yuri Tschinkel.
Heights and morphisms in number fields Manin, and Yuri Tschinkel
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.621152Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 8487d348-a673-4833-b850-3a3de8beb04b · outbound
This paper cites Intersection Theory.
Heights and morphisms in number fields Intersection Theory
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.601549Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 8b25775b-8d80-474b-b4d4-a23896d8e9fc · outbound
This paper cites H\"older estimates and uniformity in arithmetic dynamics.
Heights and morphisms in number fields H\"older estimates and uniformity in arithmetic dynamics
Reference 12
- Resolution
- verified exact
- local_arxiv, observed 2026-08-12T16:36:15.095012Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 626a7681-adb2-4fa6-a979-a1797b478610 · outbound
This paper cites an unresolved cited work.
Heights and morphisms in number fields Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T16:36:15.585868Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e2c77802-d32a-4047-9a7d-b7f4cacfe0b5 · outbound
This paper cites Counting elliptic curves with prescribed torsion.
Heights and morphisms in number fields Counting elliptic curves with prescribed torsion
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.570685Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d6671599-648f-41dc-b396-b6e348bddb35 · outbound
This paper cites Silverman.
Heights and morphisms in number fields Silverman
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.553527Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e5a81556-5757-4588-a918-a67a79336fa7 · outbound
This paper cites Minimally critical endomorphisms of P^N.
Heights and morphisms in number fields Minimally critical endomorphisms of P^N
Reference 16
- Resolution
- verified exact
- local_arxiv, observed 2026-08-12T16:36:15.068886Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 033b67f3-028b-4747-b660-8de1bd501d2f · outbound
This paper cites Explicit canonical heights for divisors relative to endomorphisms of $\mathbb{P}^N$.
Heights and morphisms in number fields Explicit canonical heights for divisors relative to endomorphisms of $\mathbb{P}^N$
Reference 17
- Resolution
- verified exact
- local_arxiv, observed 2026-08-12T16:36:15.042331Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e6f9905b-57de-4f5f-9613-bc1ff9170506 · outbound
This paper cites Computing points of bounded height in projective space over a number field.
Heights and morphisms in number fields Computing points of bounded height in projective space over a number field
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.537422Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a34422fd-8d63-4f84-b724-96a0b35fc089 · outbound
This paper cites Diophantine Geometry.
Heights and morphisms in number fields Diophantine Geometry
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.520746Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation f9f69a02-061d-4aba-8907-053379a7642e · outbound
This paper cites Arithmetic dynamics of random polynomials.
Heights and morphisms in number fields Arithmetic dynamics of random polynomials
Reference 20
- Resolution
- verified exact
- local_arxiv, observed 2026-08-12T16:36:15.017245Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a491c4cc-1864-45fa-bf62-af7f0dbac47a · outbound
This paper cites an unresolved cited work.
Heights and morphisms in number fields Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T16:36:15.503485Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 5fc68569-e185-4e65-a776-a60cf9db4c9c · outbound
This paper cites an unresolved cited work.
Heights and morphisms in number fields Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T16:36:15.486255Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4c72b6b0-5b51-4da3-9253-5b2e35e48883 · outbound
This paper cites an unresolved cited work.
Heights and morphisms in number fields Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T16:36:15.469527Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 0d346eb4-827f-493c-84dd-98fbcba61696 · outbound
This paper cites Silverman.
Heights and morphisms in number fields Silverman
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.452556Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation bd90f3d6-f0f8-4e8f-8eb2-d3480e6862fe · outbound
This paper cites Ram Murty and Jeanine Van Order.
Heights and morphisms in number fields Ram Murty and Jeanine Van Order
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.435942Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 703ba623-a4ab-41c1-8404-d7a669290713 · outbound
This paper cites an unresolved cited work.
Heights and morphisms in number fields Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T16:36:15.418133Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 7dec8840-b4bc-4837-96c9-c16f580726a8 · outbound
This paper cites Distribution of preperiodic points in one-parameter families of rational maps.
Heights and morphisms in number fields Distribution of preperiodic points in one-parameter families of rational maps
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.402472Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation eed0c3ff-360e-487f-8ddd-1cbaff076ae3 · outbound
This paper cites Effective Hilbert's Irreducibility Theorem for global fields.
Heights and morphisms in number fields Effective Hilbert's Irreducibility Theorem for global fields
Reference 28
- Resolution
- verified exact
- local_arxiv, observed 2026-08-12T16:36:14.984757Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a4edad74-bb3a-4856-8a2c-26f0a4d19b2f · outbound
This paper cites Hauteurs et mesures de Tamagawa sur les vari´ et´ es de Fano.Duke Math.
Heights and morphisms in number fields Hauteurs et mesures de Tamagawa sur les vari´ et´ es de Fano.Duke Math
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.386376Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 2357dc05-36ea-4d79-aac6-33cd77c8dd1a · outbound
This paper cites On the Foundations of Combinatorial Theory.
Heights and morphisms in number fields On the Foundations of Combinatorial Theory
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.370855Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d56d7545-5ade-49d5-8990-240f541e47a9 · outbound
This paper cites Schanuel.
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.354238Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation ad087fec-c15d-41e2-9d6a-9f6e1ab627d9 · outbound
This paper cites Heights in number fields.
Heights and morphisms in number fields Heights in number fields
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.338388Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation fd69d39f-71ef-411b-a4b0-05e4b17ae725 · outbound
This paper cites Lectures on the Mordell-Weil theorem.
Heights and morphisms in number fields Lectures on the Mordell-Weil theorem
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.321082Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 835f1388-7dcd-4d7f-9deb-f311e331fa5e · outbound
This paper cites Silverman.
Heights and morphisms in number fields Silverman
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.303825Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a044c584-1363-4d28-84f6-7303372dee8f · outbound
This paper cites On the number of quadratic polynomials with a given portrait.
Heights and morphisms in number fields On the number of quadratic polynomials with a given portrait
Reference 35
- Resolution
- verified exact
- local_arxiv, observed 2026-08-12T16:36:14.960152Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a1aaf705-505d-4e61-af41-2d9b7893e4c3 · outbound
This paper cites an unresolved cited work.
Heights and morphisms in number fields Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T16:36:15.287113Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 1f1f6e82-219e-4647-88ef-177783b28454 · outbound
This paper cites an unresolved cited work.
Heights and morphisms in number fields Unresolved cited work
Reference 37
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T16:36:15.269657Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d7041d5d-5c6c-46b6-a6d1-1e086ff08c53 · outbound
This paper cites stacks.math.columbia.edu/tag/01NE, 2018.
Heights and morphisms in number fields stacks.math.columbia.edu/tag/01NE, 2018
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.252946Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4f7252d9-a372-45e5-a71a-71a30b628eec · outbound
This paper cites Counting primitive points of bounded height.
Heights and morphisms in number fields Counting primitive points of bounded height
Reference 39
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.236290Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d0122f52-cef0-402f-8377-a6ebcef19592 · outbound
This paper cites Lipschitz class, narrow class, and counting lattice points.
Heights and morphisms in number fields Lipschitz class, narrow class, and counting lattice points
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:36:15.218816Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Pith citing papers
No inbound Pith citation observations are available.