frontiers / frontier

Erdős problems frontier

id: vfr_37aec80d874a0239
license: CC-BY-4.0
findings: 1,256
accepted core: 6
contested: 0
links: 17
sources: 1,234
evidence: 1,256
avg conf: 0.98

used by 0 · replayed by 2 producers

e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null

Source record

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manual finding

id: vs_066123dd29a9c5b4
frontier: Erdős problems frontier
type: paper

source boundary

frontier-owned

declared

finding bindings

record context

17 findings

evidence atoms

materialized

17 atoms

review context

inspectable

17 events

17 reviewable changes and 0 evaluations are attached through this source or its findings.

citation

locator

title:manual finding

imported

2026-06-10T06:44:21.845655+00:00

extraction mode

manual_curation

authors

reviewer:will-blair

caveats

No caveats recorded.

Bound findings

OBLIGATION (Erdos #124). BANKED: the reservoir criterion verified on the BEGL case {3,4,7}, k=1. OPEN: uniform L-syndeticity across all cases remains open.
theoretical · vf_0bdc86f4d9f9ea18
OBLIGATION (Erdos #203). BANKED: a partial CRT covering certificate (m + 20 prime rows, ~0.7467 density) verified (crt_partial_cover). OPEN: extend to a full cover (the verified rows do not cover all residues).
theoretical · vf_0d4ac181db98ceaa
OBLIGATION (Erdos #1093). BANKED: three delta=1 examples beyond ELS93 (k=106/126/129) verified; the density model leans finite. OPEN: prove finiteness of the delta=1 deficiency cases (the density argument is heuristic, not a proof).
theoretical · vf_279e997d3b3da2ee
The Erdős Problems database at erdosproblems.com catalogs problems posed by or jointly attributed to Paul Erdős, with public status (open, partial, solved) and citations to the original problem statement.
mechanism · vf_2b1d432fcb715fd3
OBLIGATION (Erdos #1094). BANKED: the 14 ELS exceptions enumerated provably-complete to k<=40 (binom_exception_enum). OPEN: extend the complete enumeration / prove finiteness of the exception set for all k.
theoretical · vf_2d4edfce58578092
OBLIGATION (Erdos #700). BANKED: f(n)=min gcd(n,C(n,k)) recomputed for the cited cases (semiprime and prime-power families). OPEN: characterize f(n) in general beyond the verified families.
theoretical · vf_2db3437d1512c222
OBLIGATION (Erdos #307). BANKED: the congruence-barrier construction verified. OPEN: the unconditional bound remains open.
theoretical · vf_523a610fc3947249
OBLIGATION (Erdos #396). BANKED: the GPT-Pro reduction is banked and re-verified (obstruction map: HONEST, no solve). OPEN: the reduction does not solve #396; the solve remains open.
theoretical · vf_7cb1a5b07207120e
OBLIGATION (Erdos #993). BANKED: the banked unimodality result for the tree/forest case verified (frozen kernel). OPEN: the general Alavi-Erdos unimodality conjecture is open.
theoretical · vf_7eba52ea8a9bc742
OBLIGATION (Erdos #319). BANKED: the counting step of the upper bound corroborated numerically. OPEN: the full upper bound is not established by the numerics alone.
theoretical · vf_a9a5b1e0dbdc9da4
OBLIGATION (Erdos #647). BANKED: the prime / forced-divisor channel is provably exhausted (banked obstruction_map + Erdos647Obstruction.lean). OPEN: a different channel is required; the prime channel cannot close it (stop grinding it).
theoretical · vf_ac4c84ea5e608bb7
OBLIGATION (Erdos #1056). BANKED: explicit cut-equality certificates verified for every k in 2..14 (interval_product witnesses). OPEN: the problem asks for EVERY k; a uniform construction or proof for all k remains open.
theoretical · vf_ae08f178d51bb99e
OBLIGATION (Erdos #684). BANKED: f(M_K-1) > K verified for K=3..12 via Kummer no-carry (effective, subsequential lower bound). OPEN: promote the subsequential bound to the full claim for all n.
theoretical · vf_ba50ac1f1f60aa27
OBLIGATION (Erdos #366). BANKED: the unconditional Mordell-curve reduction + Pell correction + the two analytic walls verified. OPEN: the analytic walls block an unconditional bound; closing them is open.
theoretical · vf_cd5fe218ed92cc31
OBLIGATION (Erdos #617). BANKED: K25 balanced-coloring construction known; the K26 finite case is the first open case and reduces to a SAT instance. OPEN: produce the LRAT/RAT certificate for the K26 SAT encoding and re-check it with `vela reproduce` (unsat_cert); the symmetry-breaking step needs RAT, beyond the current RUP checker.
theoretical · vf_da8d51a6cae5ec11
OBLIGATION (Erdos #699). BANKED: the central-doubling reduction + CRT obstruction verified; the two arms provably do not meet. OPEN: the gap between the arms is the open obstruction.
theoretical · vf_eb741f9becc60879
OBLIGATION (Erdos #488). BANKED: per-fixed-A exact decision certificates (7500+ antichains, zero counterexamples). OPEN: no uniform proof: the per-A certificates do not combine into a statement for all A.
theoretical · vf_ef7066987d658f0e

Evidence atoms

vea_0d88f13fa63b9f37theoretical · unknown
OBLIGATION (Erdos #1056). BANKED: explicit cut-equality certificates verified for every k in 2..14 (interval_product witnesses). OPEN: the problem asks for EVERY k; a uniform construction or proof for all k remains open.
vea_20582669f252159btheoretical · unknown
OBLIGATION (Erdos #699). BANKED: the central-doubling reduction + CRT obstruction verified; the two arms provably do not meet. OPEN: the gap between the arms is the open obstruction.
vea_2ae395d988ffd533theoretical · unknown
OBLIGATION (Erdos #396). BANKED: the GPT-Pro reduction is banked and re-verified (obstruction map: HONEST, no solve). OPEN: the reduction does not solve #396; the solve remains open.
vea_57a1168dd7e45a65theoretical · unknown
OBLIGATION (Erdos #488). BANKED: per-fixed-A exact decision certificates (7500+ antichains, zero counterexamples). OPEN: no uniform proof: the per-A certificates do not combine into a statement for all A.
vea_6d928d763423f30ctheoretical · unknown
OBLIGATION (Erdos #700). BANKED: f(n)=min gcd(n,C(n,k)) recomputed for the cited cases (semiprime and prime-power families). OPEN: characterize f(n) in general beyond the verified families.
vea_76542d9bfb9d573btheoretical · unknown
OBLIGATION (Erdos #307). BANKED: the congruence-barrier construction verified. OPEN: the unconditional bound remains open.
vea_837ac972afed75f3theoretical · unknown
OBLIGATION (Erdos #319). BANKED: the counting step of the upper bound corroborated numerically. OPEN: the full upper bound is not established by the numerics alone.
vea_93fb4f516f9e9500theoretical · unknown
OBLIGATION (Erdos #203). BANKED: a partial CRT covering certificate (m + 20 prime rows, ~0.7467 density) verified (crt_partial_cover). OPEN: extend to a full cover (the verified rows do not cover all residues).
vea_a0001b9783109c5dtheoretical · unknown
OBLIGATION (Erdos #647). BANKED: the prime / forced-divisor channel is provably exhausted (banked obstruction_map + Erdos647Obstruction.lean). OPEN: a different channel is required; the prime channel cannot close it (stop grinding it).
vea_a1a5534e334a5546theoretical · unknown
OBLIGATION (Erdos #684). BANKED: f(M_K-1) > K verified for K=3..12 via Kummer no-carry (effective, subsequential lower bound). OPEN: promote the subsequential bound to the full claim for all n.
vea_a73486f8a4f7e1fctheoretical · unknown
OBLIGATION (Erdos #124). BANKED: the reservoir criterion verified on the BEGL case {3,4,7}, k=1. OPEN: uniform L-syndeticity across all cases remains open.
vea_ad089b920d3b7fb5theoretical · unknown
OBLIGATION (Erdos #617). BANKED: K25 balanced-coloring construction known; the K26 finite case is the first open case and reduces to a SAT instance. OPEN: produce the LRAT/RAT certificate for the K26 SAT encoding and re-check it with `vela reproduce` (unsat_cert); the symmetry-breaking step needs RAT, beyond the current RUP checker.
vea_b9bca5061ddde1b4theoretical · unknown
The Erdős Problems database at erdosproblems.com catalogs problems posed by or jointly attributed to Paul Erdős, with public status (open, partial, solved) and citations to the original problem statement.
vea_e4d9918d20e1fd2atheoretical · unknown
OBLIGATION (Erdos #1094). BANKED: the 14 ELS exceptions enumerated provably-complete to k<=40 (binom_exception_enum). OPEN: extend the complete enumeration / prove finiteness of the exception set for all k.
vea_eb4595aafa160878theoretical · unknown
OBLIGATION (Erdos #366). BANKED: the unconditional Mordell-curve reduction + Pell correction + the two analytic walls verified. OPEN: the analytic walls block an unconditional bound; closing them is open.
vea_f86597f64a1e1319theoretical · unknown
OBLIGATION (Erdos #1093). BANKED: three delta=1 examples beyond ELS93 (k=106/126/129) verified; the density model leans finite. OPEN: prove finiteness of the delta=1 deficiency cases (the density argument is heuristic, not a proof).
vea_fa2806fa4d1fbdb0theoretical · unknown
OBLIGATION (Erdos #993). BANKED: the banked unimodality result for the tree/forest case verified (frozen kernel). OPEN: the general Alavi-Erdos unimodality conjecture is open.

Review, event, and evaluation records

events

vev_06299e1fa4b38b2cfinding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10
vev_085d96acc5cb0f61finding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10
vev_0c6f574238aaa5befinding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10
vev_0dede50cc58aa569finding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10
vev_4361e1a9e622891efinding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10
vev_47dd109deff7ad43finding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10
vev_4ed0566c6d8462c4finding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10
vev_5a8a4e9a023334e3finding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10
vev_6cb80630f2af6cf6finding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10
vev_73d515a0b0ece58efinding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10
vev_74a9731ebe1fb815finding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10
vev_837a5c12f0a2cd04finding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10
vev_936e368f6276980afinding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10
vev_a912b78163431120finding.asserted
Manual finding added to frontier state
reviewer:vela-curation-bot · 2026-05-10
vev_ab0ff952a11cc759finding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10
vev_cce6112578768663finding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10
vev_fe012295f0f30fa7finding.asserted
Manual finding added to frontier state
reviewer:will-blair · 2026-06-10

reviewable changes

vpr_0cfb5a79b5eb3fdafinding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
vpr_1890ac65b9adb8ebfinding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
vpr_2e31da48fef48754finding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
vpr_313d8eb17163ed01finding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
vpr_3f1bbe8699d6b485finding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
vpr_491ca506a4c62af8finding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
vpr_59a39849c32ca346finding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
vpr_6ce632e3d52850dbfinding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
vpr_6dbe94758958b601finding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
vpr_7af014cbf9b80043finding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
vpr_93b3eb684ddd0173finding.add
Manual finding added to frontier state
applied · reviewer:vela-curation-bot · 2026-05-10
vpr_b1a3dd0af8b0ed35finding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
vpr_e48e6e03c450478dfinding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
vpr_edc38cb972d92315finding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
vpr_f553d57efcdad26bfinding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
vpr_fca9c6018554a986finding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10
vpr_fdcdbeece3cb0dd4finding.add
Manual finding added to frontier state
applied · reviewer:will-blair · 2026-06-10

evaluations

No evaluation rows are attached.